Journal of Computational Physics, ISSN 0021-9991, 12/2016, Volume 327, pp. 252 - 269

The aim of this paper is to build and validate some explicit high-order schemes, both in space and time, for simulating the dynamics of systems of nonlinear...

Gross–Pitaevskii equation | Pseudo-spectral schemes | Adaptive time stepping | Dynamics | Bose–Einstein condensates | Time-splitting | Nonlinear Schrödinger equation | Spin-orbit | High-order discretization | IMplicit–EXplicit schemes | STATES | RUNGE-KUTTA METHODS | Nonlinear Schrodinger equation | Gross-Pitaevskii equation | IMplicit-EXplicit schemes | PHYSICS, MATHEMATICAL | SPLITTING METHODS | MATLAB TOOLBOX | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Bose-Einstein condensates | COMPUTATION | EFFICIENT | GPELAB | Numerical Analysis | Analysis of PDEs | Mathematics

Gross–Pitaevskii equation | Pseudo-spectral schemes | Adaptive time stepping | Dynamics | Bose–Einstein condensates | Time-splitting | Nonlinear Schrödinger equation | Spin-orbit | High-order discretization | IMplicit–EXplicit schemes | STATES | RUNGE-KUTTA METHODS | Nonlinear Schrodinger equation | Gross-Pitaevskii equation | IMplicit-EXplicit schemes | PHYSICS, MATHEMATICAL | SPLITTING METHODS | MATLAB TOOLBOX | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Bose-Einstein condensates | COMPUTATION | EFFICIENT | GPELAB | Numerical Analysis | Analysis of PDEs | Mathematics

Journal Article

Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 07/2014, Volume 24, Issue 8, pp. 1575 - 1619

We present Finite Volume methods for diffusion equations on generic meshes, that received important coverage in the last decade or so. After introducing the...

Elliptic equation | Discrete duality finite volume schemes | Coercivity | Minimum and maximum principles | Multi-point flux approximation | Review | Monotony | Finite volume schemes | Hybrid mimetic mixed methods | Convergence analysis | DISCRETE DUALITY | MATHEMATICS, APPLIED | coercivity | hybrid mimetic mixed methods | multi-point flux approximation | monotony | GENERAL 2D MESHES | convergence analysis | MULTIPOINT FLUX APPROXIMATION | QUADRILATERAL GRIDS | TENSOR PRESSURE EQUATION | DIFFERENCE METHOD | discrete duality finite volume schemes | UNSTRUCTURED POLYHEDRAL MESHES | NONLINEAR ELLIPTIC-EQUATIONS | POLYGONAL MESHES | finite volume schemes | minimum and maximum principles | CENTERED GALERKIN METHODS | elliptic equation | Mathematics - Numerical Analysis

Elliptic equation | Discrete duality finite volume schemes | Coercivity | Minimum and maximum principles | Multi-point flux approximation | Review | Monotony | Finite volume schemes | Hybrid mimetic mixed methods | Convergence analysis | DISCRETE DUALITY | MATHEMATICS, APPLIED | coercivity | hybrid mimetic mixed methods | multi-point flux approximation | monotony | GENERAL 2D MESHES | convergence analysis | MULTIPOINT FLUX APPROXIMATION | QUADRILATERAL GRIDS | TENSOR PRESSURE EQUATION | DIFFERENCE METHOD | discrete duality finite volume schemes | UNSTRUCTURED POLYHEDRAL MESHES | NONLINEAR ELLIPTIC-EQUATIONS | POLYGONAL MESHES | finite volume schemes | minimum and maximum principles | CENTERED GALERKIN METHODS | elliptic equation | Mathematics - Numerical Analysis

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 02/2016, Volume 444, pp. 1 - 8

The goal of this work is to determine classes of traveling solitary wave solutions for Lattice Boltzmann schemes by means of a hyperbolic ansatz. It is shown...

Structural stability | Solitary waves | Lattice Boltzmann schemes | SOLITARY WAVE SOLUTIONS | DE-VRIES EQUATION | PHYSICS, MULTIDISCIPLINARY

Structural stability | Solitary waves | Lattice Boltzmann schemes | SOLITARY WAVE SOLUTIONS | DE-VRIES EQUATION | PHYSICS, MULTIDISCIPLINARY

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 11/2018, Volume 372, pp. 178 - 201

In this work, we consider the development of implicit-explicit total variation diminishing (TVD) methods (also termed SSP: strong stability preserving) for the...

Low Mach | SSP-TVD | IMEX schemes | High-order | Asymptotic preserving | Hyperbolic | NUMBER LIMIT | RUNGE-KUTTA METHODS | HYPERBOLIC SYSTEMS | ASYMPTOTIC PRESERVING SCHEME | INCOMPRESSIBLE LIMIT | GAS-DYNAMICS EQUATIONS | PHYSICS, MATHEMATICAL | CONVERGENCE ACCELERATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | ISENTROPIC EULER | UNSTRUCTURED MESHES | Mathematics - Numerical Analysis | Numerical Analysis | Analysis of PDEs | Mathematics

Low Mach | SSP-TVD | IMEX schemes | High-order | Asymptotic preserving | Hyperbolic | NUMBER LIMIT | RUNGE-KUTTA METHODS | HYPERBOLIC SYSTEMS | ASYMPTOTIC PRESERVING SCHEME | INCOMPRESSIBLE LIMIT | GAS-DYNAMICS EQUATIONS | PHYSICS, MATHEMATICAL | CONVERGENCE ACCELERATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | ISENTROPIC EULER | UNSTRUCTURED MESHES | Mathematics - Numerical Analysis | Numerical Analysis | Analysis of PDEs | Mathematics

Journal Article

SIAM JOURNAL ON SCIENTIFIC COMPUTING, ISSN 1064-8275, 2019, Volume 41, Issue 3, pp. A1500 - A1526

We present a positive-and asymptotic-preserving numerical scheme for solving linear kinetic transport equations that relax to a diffusive equation in the limit...

asymptotic-preserving schemes | MATHEMATICS, APPLIED | positive-preserving schemes | DG-IMEX SCHEMES | AP SCHEMES | RUNGE-KUTTA METHODS | WELL-BALANCED SCHEMES | finite difference methods | diffusion limit | DIFFUSIVE RELAXATION SCHEMES | RADIATIVE-TRANSFER | kinetic transport equations | BOLTZMANN-EQUATION | MOMENT CLOSURES | CONSERVATION-LAWS | OPTICALLY THICK | BASIC BIOLOGICAL SCIENCES | asymptotic | nite difference methods | preserving schemes

asymptotic-preserving schemes | MATHEMATICS, APPLIED | positive-preserving schemes | DG-IMEX SCHEMES | AP SCHEMES | RUNGE-KUTTA METHODS | WELL-BALANCED SCHEMES | finite difference methods | diffusion limit | DIFFUSIVE RELAXATION SCHEMES | RADIATIVE-TRANSFER | kinetic transport equations | BOLTZMANN-EQUATION | MOMENT CLOSURES | CONSERVATION-LAWS | OPTICALLY THICK | BASIC BIOLOGICAL SCIENCES | asymptotic | nite difference methods | preserving schemes

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2017, Volume 330, pp. 401 - 435

We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer–Nunziato two-phase flow model. This relaxation scheme is...

Energy–entropy duality | Riemann problem | Riemann solvers | Relaxation techniques | Finite volumes | Hyperbolic PDEs | Entropy-satisfying methods | Compressible multi-phase flows | Energy-entropy duality | COMPRESSIBLE 2-PHASE FLOW | PHASE-TRANSITIONS | PHYSICS, MATHEMATICAL | GODUNOV METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DDT | CONSTITUTIVE-EQUATIONS | MIXTURE THEORY | CONSERVATION-LAWS | Nuclear industry | Models | Numerical analysis | Analysis | Relaxation | Mechanics | Mechanics of the fluids | Mathematics | Numerical Analysis | Analysis of PDEs | Physics | NUMERICAL ANALYSIS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | APPROXIMATIONS | NUCLEAR INDUSTRY | STABILITY | RELAXATION | COMPARATIVE EVALUATIONS | TWO-PHASE FLOW | ISENTROPIC PROCESSES | COMPUTERIZED SIMULATION | DENSITY | MATHEMATICAL SOLUTIONS | PARTIAL DIFFERENTIAL EQUATIONS | CONVERGENCE | SOUND WAVES | EQUATIONS OF STATE | FLOW MODELS | MULTIPHASE FLOW | ENTROPY

Energy–entropy duality | Riemann problem | Riemann solvers | Relaxation techniques | Finite volumes | Hyperbolic PDEs | Entropy-satisfying methods | Compressible multi-phase flows | Energy-entropy duality | COMPRESSIBLE 2-PHASE FLOW | PHASE-TRANSITIONS | PHYSICS, MATHEMATICAL | GODUNOV METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DDT | CONSTITUTIVE-EQUATIONS | MIXTURE THEORY | CONSERVATION-LAWS | Nuclear industry | Models | Numerical analysis | Analysis | Relaxation | Mechanics | Mechanics of the fluids | Mathematics | Numerical Analysis | Analysis of PDEs | Physics | NUMERICAL ANALYSIS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | APPROXIMATIONS | NUCLEAR INDUSTRY | STABILITY | RELAXATION | COMPARATIVE EVALUATIONS | TWO-PHASE FLOW | ISENTROPIC PROCESSES | COMPUTERIZED SIMULATION | DENSITY | MATHEMATICAL SOLUTIONS | PARTIAL DIFFERENTIAL EQUATIONS | CONVERGENCE | SOUND WAVES | EQUATIONS OF STATE | FLOW MODELS | MULTIPHASE FLOW | ENTROPY

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 01/2016, Volume 305, pp. 44 - 62

High-order numerical methods for solving time-dependent acoustic–elastic coupled problems are introduced. These methods, based on Finite Element techniques,...

Elastic–acoustic | High-order schemes | Finite element methods | Wave propagation problems | Coupled problems | Non-conforming meshes | Elastic-acoustic | CONSERVATIVE LOAD-TRANSFER | DISCONTINUOUS GALERKIN METHOD | FLUID-STRUCTURE INTERACTION | FORMULATION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SOLID INTERFACE | MEDIA | ELASTODYNAMICS | NONMATCHING MESHES | SCATTERING | WAVE-PROPAGATION | Finite element method | Time dependence | Discretization | Mathematical analysis | Media | Joining | Coupling | Curved | Analysis of PDEs | Mathematics

Elastic–acoustic | High-order schemes | Finite element methods | Wave propagation problems | Coupled problems | Non-conforming meshes | Elastic-acoustic | CONSERVATIVE LOAD-TRANSFER | DISCONTINUOUS GALERKIN METHOD | FLUID-STRUCTURE INTERACTION | FORMULATION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SOLID INTERFACE | MEDIA | ELASTODYNAMICS | NONMATCHING MESHES | SCATTERING | WAVE-PROPAGATION | Finite element method | Time dependence | Discretization | Mathematical analysis | Media | Joining | Coupling | Curved | Analysis of PDEs | Mathematics

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2013, Volume 51, Issue 2, pp. 840 - 863

We prove enhanced error estimates for high order semi-Lagrangian discretizations of the Vlasov-Poisson equation. It provides new insights into optimal...

Interpolation | Error rates | Advection | Mathematical integrals | Analytical estimating | Truncation errors | Mathematics | Lagrangian function | Electric fields | Stencils | Semi-Lagrangian scheme | Vlasov-Poisson | Advection equation | SYSTEM | LINEAR ADVECTION | MATHEMATICS, APPLIED | semi-Lagrangian scheme | STABILITY | advection equation | NORM | DIFFERENCE-SCHEMES | ACCURACY | Errors | Numerical analysis | Discretization | Mathematical analysis | Strategy | Estimates | Optimization | Convergence | Analysis of PDEs

Interpolation | Error rates | Advection | Mathematical integrals | Analytical estimating | Truncation errors | Mathematics | Lagrangian function | Electric fields | Stencils | Semi-Lagrangian scheme | Vlasov-Poisson | Advection equation | SYSTEM | LINEAR ADVECTION | MATHEMATICS, APPLIED | semi-Lagrangian scheme | STABILITY | advection equation | NORM | DIFFERENCE-SCHEMES | ACCURACY | Errors | Numerical analysis | Discretization | Mathematical analysis | Strategy | Estimates | Optimization | Convergence | Analysis of PDEs

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2011, Volume 230, Issue 8, pp. 3035 - 3061

Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume...

Water waves | Finite volume method | Dispersive waves | Runup | Solitary waves | BOUNDARY-VALUE-PROBLEMS | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATIONS | NONOSCILLATORY SCHEMES | NUMERICAL-ANALYSIS | AMPLITUDE LONG WAVES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DISCONTINUOUS GALERKIN METHODS | BOUSSINESQ-TYPE EQUATIONS | TIME DISCRETIZATION METHODS | HYPERBOLIC CONSERVATION-LAWS | Analysis | Wave propagation | Conservation laws | Boussinesq equations | Approximation | Mathematical analysis | Nonlinearity | Mathematical models | Fluid Dynamics | Computational Physics | Pattern Formation and Solitons | Analysis of PDEs | Mathematics | Nonlinear Sciences | Sciences of the Universe | Physics | Atmospheric and Oceanic Physics | Numerical Analysis | Mechanics | Mechanics of the fluids | Reactive fluid environment | Fluids mechanics | Ocean, Atmosphere | Engineering Sciences

Water waves | Finite volume method | Dispersive waves | Runup | Solitary waves | BOUNDARY-VALUE-PROBLEMS | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATIONS | NONOSCILLATORY SCHEMES | NUMERICAL-ANALYSIS | AMPLITUDE LONG WAVES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DISCONTINUOUS GALERKIN METHODS | BOUSSINESQ-TYPE EQUATIONS | TIME DISCRETIZATION METHODS | HYPERBOLIC CONSERVATION-LAWS | Analysis | Wave propagation | Conservation laws | Boussinesq equations | Approximation | Mathematical analysis | Nonlinearity | Mathematical models | Fluid Dynamics | Computational Physics | Pattern Formation and Solitons | Analysis of PDEs | Mathematics | Nonlinear Sciences | Sciences of the Universe | Physics | Atmospheric and Oceanic Physics | Numerical Analysis | Mechanics | Mechanics of the fluids | Reactive fluid environment | Fluids mechanics | Ocean, Atmosphere | Engineering Sciences

Journal Article

Computer Physics Communications, ISSN 0010-4655, 01/2019, Volume 234, pp. 40 - 54

Partial differential equations (p.d.e) equipped with spatial derivatives of fractional order capture anomalous transport behaviors observed in diverse fields...

Multiple-Relaxation-Time | Lattice Boltzmann method | Stable process | Fractional advection–diffusion equation | Random walk | CONVECTION | STABILITY | CALCULUS | PHYSICS, MATHEMATICAL | TRANSPORT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DISPERSION-EQUATION | Fractional advection-diffusion equation | RANDOM-WALK | LEVY MOTION | PHASE-FIELD MODEL | Anisotropy | Differential equations | Computational Physics | Mathematics | Analysis of PDEs | Physics

Multiple-Relaxation-Time | Lattice Boltzmann method | Stable process | Fractional advection–diffusion equation | Random walk | CONVECTION | STABILITY | CALCULUS | PHYSICS, MATHEMATICAL | TRANSPORT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DISPERSION-EQUATION | Fractional advection-diffusion equation | RANDOM-WALK | LEVY MOTION | PHASE-FIELD MODEL | Anisotropy | Differential equations | Computational Physics | Mathematics | Analysis of PDEs | Physics

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2019

One of the most fascinating phenomena observed in reaction-diffusion systems is the emergence of segregated solutions, i.e. population densities with disjoint...

Analysis of PDEs | Mathematics

Analysis of PDEs | Mathematics

Journal Article

Computers and Fluids, ISSN 0045-7930, 10/2017, Volume 156, pp. 329 - 342

Many applications involve partial differential equations which admits nontrivial steady state solutions. The design of schemes which are able to describe...

Fokker–Planck equations | Well-balanced schemes | Shallow-water | Steady-states preserving | Micro-macro decomposition | KINETIC-EQUATIONS | CONVECTION | ALGORITHMS | SOURCE TERMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | HIGH-RESOLUTION SCHEMES | BOLTZMANN-EQUATION | Fokker-Planck equations | DIFFUSION | HYPERBOLIC CONSERVATION-LAWS | Environmental law | Differential equations | Analysis of PDEs | Mathematics

Fokker–Planck equations | Well-balanced schemes | Shallow-water | Steady-states preserving | Micro-macro decomposition | KINETIC-EQUATIONS | CONVECTION | ALGORITHMS | SOURCE TERMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | HIGH-RESOLUTION SCHEMES | BOLTZMANN-EQUATION | Fokker-Planck equations | DIFFUSION | HYPERBOLIC CONSERVATION-LAWS | Environmental law | Differential equations | Analysis of PDEs | Mathematics

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 05/2014, Volume 75, Issue 2, pp. 81 - 102

SUMMARYWe are concerned with a coupled system describing the interaction between suspended particles and a dense fluid. The particles are modeled by a kinetic...

asymptotic‐preserving schemes | hydrodynamic regimes | kinetic‐fluid model | fluid–particles flows | variable density incompressible flow | Kinetic-fluid model | Fluid-particles flows | Asymptotic-preserving schemes | Hydrodynamic regimes | Variable density incompressible flow | asymptotic-preserving schemes | PARTICLES FLOWS | STOKES SYSTEM | AP SCHEMES | fluid-particles flows | kinetic-fluid model | PHYSICS, FLUIDS & PLASMAS | EQUATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | REGIME | PARTICULATE FLOWS | NUMERICAL-SIMULATION | Design engineering | Fluids | Computational fluid dynamics | Asymptotic properties | Fluid flow | Mathematical models | Density | Navier-Stokes equations

asymptotic‐preserving schemes | hydrodynamic regimes | kinetic‐fluid model | fluid–particles flows | variable density incompressible flow | Kinetic-fluid model | Fluid-particles flows | Asymptotic-preserving schemes | Hydrodynamic regimes | Variable density incompressible flow | asymptotic-preserving schemes | PARTICLES FLOWS | STOKES SYSTEM | AP SCHEMES | fluid-particles flows | kinetic-fluid model | PHYSICS, FLUIDS & PLASMAS | EQUATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | REGIME | PARTICULATE FLOWS | NUMERICAL-SIMULATION | Design engineering | Fluids | Computational fluid dynamics | Asymptotic properties | Fluid flow | Mathematical models | Density | Navier-Stokes equations

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2017, Volume 49, Issue 2, pp. 1385 - 1418

Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport...

Gradient flows | Gamma-convergence | Optimal transport | Convex analysis | Entropic regularization | MATHEMATICS, APPLIED | DOUBLY STOCHASTIC MATRICES | APPROXIMATION | gamma-convergence | optimal transport | entropic regularization | SCHRODINGER-PROBLEM | MODEL | convex analysis | gradient flows | DIFFUSION-EQUATIONS | STEEPEST DESCENT | WASSERSTEIN SPACE | Mathematics | Optimization and Control | Analysis of PDEs | Numerical Analysis

Gradient flows | Gamma-convergence | Optimal transport | Convex analysis | Entropic regularization | MATHEMATICS, APPLIED | DOUBLY STOCHASTIC MATRICES | APPROXIMATION | gamma-convergence | optimal transport | entropic regularization | SCHRODINGER-PROBLEM | MODEL | convex analysis | gradient flows | DIFFUSION-EQUATIONS | STEEPEST DESCENT | WASSERSTEIN SPACE | Mathematics | Optimization and Control | Analysis of PDEs | Numerical Analysis

Journal Article

IMA Journal of Numerical Analysis, ISSN 0272-4979, 10/2016, Volume 36, Issue 4, pp. 1804 - 1841

This paper deals with the numerical integration of well-posed multiscale systems of ODEs or evolutionary partial differential equations (PDEs). As these...

asymptotic error | subcycling | longtime asymptotics | è-schemes | asymptotic order | Lie- and Strang-splitting schemes | MATHEMATICS, APPLIED | KINETIC-EQUATIONS | DIFFUSION ASYMPTOTICS | theta-schemes | MODEL | SIMULATION | FLUID | WAVE-EQUATIONS | STRUCTURAL DYNAMICS | Analysis of PDEs | Mathematics

asymptotic error | subcycling | longtime asymptotics | è-schemes | asymptotic order | Lie- and Strang-splitting schemes | MATHEMATICS, APPLIED | KINETIC-EQUATIONS | DIFFUSION ASYMPTOTICS | theta-schemes | MODEL | SIMULATION | FLUID | WAVE-EQUATIONS | STRUCTURAL DYNAMICS | Analysis of PDEs | Mathematics

Journal Article

European Journal of Applied Mathematics, ISSN 0956-7925, 2018, pp. 1 - 30

The Wasserstein gradient flow structure of the partial differential equation system governing multiphase flows in porous media was recently highlighted in...

Multiphase porous media flows | Wasserstein gradient flow | augmented Lagrangian method | finite volumes | minimising movement scheme | Numerical Analysis | Analysis of PDEs | Mathematics

Multiphase porous media flows | Wasserstein gradient flow | augmented Lagrangian method | finite volumes | minimising movement scheme | Numerical Analysis | Analysis of PDEs | Mathematics

Journal Article

SIAM Review, ISSN 0036-1445, 2018, Volume 60, Issue 3, pp. 595 - 625

Quantifying the uncertainty of Lagrangian motion can be performed by solving a large number of ordinary differential equations with random velocities or,...

Stochastic advection | Uncertainty quantification | Dynamically orthogonal decomposition | Lagrangian coherent structures | Flow-map | Singular value decomposition | MATHEMATICS, APPLIED | uncertainty quantification | dynamically orthogonal decomposition | EQUATIONS | DECOMPOSITION | SUBSPACE STATISTICAL ESTIMATION | stochastic advection | VARIABILITY | flow-map | NAVIER-STOKES | DATA ASSIMILATION | MODEL-REDUCTION | ERROR | MULTIVARIATE GEOPHYSICAL FIELDS | SIMULATIONS | singular value decomposition | Dynamical Systems | Mathematics | Differential Geometry | Analysis of PDEs | Numerical Analysis

Stochastic advection | Uncertainty quantification | Dynamically orthogonal decomposition | Lagrangian coherent structures | Flow-map | Singular value decomposition | MATHEMATICS, APPLIED | uncertainty quantification | dynamically orthogonal decomposition | EQUATIONS | DECOMPOSITION | SUBSPACE STATISTICAL ESTIMATION | stochastic advection | VARIABILITY | flow-map | NAVIER-STOKES | DATA ASSIMILATION | MODEL-REDUCTION | ERROR | MULTIVARIATE GEOPHYSICAL FIELDS | SIMULATIONS | singular value decomposition | Dynamical Systems | Mathematics | Differential Geometry | Analysis of PDEs | Numerical Analysis

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 11/2016, Volume 85, Issue 302, pp. 2651 - 2685

In this article we propose a unified analysis for conforming and non-conforming finite element methods that provides a partial answer to the problem of...

DISCRETE COMPACTNESS | MATHEMATICS, APPLIED | PENALTY | GRIDS | EIGENVALUE PROBLEMS | APPROXIMATION | ELECTROMAGNETICS | CONVERGENCE | MIXED FINITE-ELEMENTS | ELEMENT EXTERIOR CALCULUS | DISCRETIZATIONS | Numerical Analysis | Analysis of PDEs | Mathematics

DISCRETE COMPACTNESS | MATHEMATICS, APPLIED | PENALTY | GRIDS | EIGENVALUE PROBLEMS | APPROXIMATION | ELECTROMAGNETICS | CONVERGENCE | MIXED FINITE-ELEMENTS | ELEMENT EXTERIOR CALCULUS | DISCRETIZATIONS | Numerical Analysis | Analysis of PDEs | Mathematics

Journal Article