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2011, Chapman & Hall/CRC numerical analysis and scientific computation series, ISBN 9781439821589, xx, 463

.... The methods presented are similar to finite elements but more adept at solving analytic problems with singularities over irregularly shaped yet analytically described regions...

Numerical solutions | Galerkin methods | Differential equations

Numerical solutions | Galerkin methods | Differential equations

Book

01/2019, ISBN 3038976679

.... The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features...

structured matrices | curl | numerical methods | time fractional differential equations | hierarchical splines | finite difference methods | null-space | highly oscillatory problems | stochastic Volterra integral equations | differential equations | displacement rank | constrained Hamiltonian problems | Hermite | hyperbolic partial differential equations | higher-order finite element methods | continuous geometric average | Volterra integro | spectral (eigenvalue) and singular value distributions | generalized locally Toeplitz sequences | Obreshkov methods | B-spline | discontinuous Galerkin methods | adaptive methods | Cholesky factorization | energy-conserving methods | order | collocation method | Poisson problems | time harmonic Maxwell’s equations and magnetostatic problems | tree | multistep methods | stochastic differential equations | optimal basis | finite difference method | elementary differential | gradient system | Runge | conservative problems | line integral methods | stochastic multistep methods | Hamiltonian Boundary Value Methods | Kutta | limited memory | boundary element method | convergence | analytical solution | preconditioners | asymptotic stability | collocation methods | histogram specification | local refinement | edge-preserving smoothing | numerical analysis | THB-splines | BS methods | barrier options | stump | shock waves and discontinuities | mean-square stability | Volterra integral equations | high order discontinuous Galerkin finite element schemes | B-splines | vectorization and parallelization | initial value problems | one-step methods | scientific computing | fractional derivative | linear systems | Hamiltonian problems | low rank completion | ordinary differential equations | mixed-index problems | edge-histogram | Hamiltonian PDEs | matrix ODEs | HBVMs | floating strike Asian options | generalized Schur algorithm | Galerkin method | symplecticity | high performance computing | isogeometric analysis | discretization of systems of differential equations | curl operator

structured matrices | curl | numerical methods | time fractional differential equations | hierarchical splines | finite difference methods | null-space | highly oscillatory problems | stochastic Volterra integral equations | differential equations | displacement rank | constrained Hamiltonian problems | Hermite | hyperbolic partial differential equations | higher-order finite element methods | continuous geometric average | Volterra integro | spectral (eigenvalue) and singular value distributions | generalized locally Toeplitz sequences | Obreshkov methods | B-spline | discontinuous Galerkin methods | adaptive methods | Cholesky factorization | energy-conserving methods | order | collocation method | Poisson problems | time harmonic Maxwell’s equations and magnetostatic problems | tree | multistep methods | stochastic differential equations | optimal basis | finite difference method | elementary differential | gradient system | Runge | conservative problems | line integral methods | stochastic multistep methods | Hamiltonian Boundary Value Methods | Kutta | limited memory | boundary element method | convergence | analytical solution | preconditioners | asymptotic stability | collocation methods | histogram specification | local refinement | edge-preserving smoothing | numerical analysis | THB-splines | BS methods | barrier options | stump | shock waves and discontinuities | mean-square stability | Volterra integral equations | high order discontinuous Galerkin finite element schemes | B-splines | vectorization and parallelization | initial value problems | one-step methods | scientific computing | fractional derivative | linear systems | Hamiltonian problems | low rank completion | ordinary differential equations | mixed-index problems | edge-histogram | Hamiltonian PDEs | matrix ODEs | HBVMs | floating strike Asian options | generalized Schur algorithm | Galerkin method | symplecticity | high performance computing | isogeometric analysis | discretization of systems of differential equations | curl operator

eBook

2012, 1. Aufl., ISBN 9780470572375, xvi, 335

"This is the first book to specifically address the explicit finite element method for nonlinear transient dynamics...

Finite element method | Numerical analysis | MATHEMATICS / Mathematical Analysis | Mathematics | Finite Mathematics

Finite element method | Numerical analysis | MATHEMATICS / Mathematical Analysis | Mathematics | Finite Mathematics

Book

SIAM journal on numerical analysis, ISSN 1095-7170, 01/2014, Volume 52, Issue 6, pp. 2599 - 2622

In this paper, a new alternating direction implicit Galerkin–Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed...

Hypergeometric functions | Error rates | Approximation | Porous materials | Numerical methods | Differential equations | Reaction diffusion equations | Legendre polynomials | Spectral methods | Finite difference methods | Riesz space fractional reaction-diffusion equation | Fractional FitzHugh-Nagumo model | Alternating direction implicit method | Legendre spectral method | Stability and convergence | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Nodular iron | Nonlinearity | Mathematical models | Reaction-diffusion equations | Two dimensional | Galerkin methods | Convergence

Hypergeometric functions | Error rates | Approximation | Porous materials | Numerical methods | Differential equations | Reaction diffusion equations | Legendre polynomials | Spectral methods | Finite difference methods | Riesz space fractional reaction-diffusion equation | Fractional FitzHugh-Nagumo model | Alternating direction implicit method | Legendre spectral method | Stability and convergence | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Nodular iron | Nonlinearity | Mathematical models | Reaction-diffusion equations | Two dimensional | Galerkin methods | Convergence

Journal Article

International journal for numerical methods in engineering, ISSN 0029-5981, 10/2008, Volume 76, Issue 1, pp. 56 - 83

An improvement to the classical finite element (FE) method is proposed. It is able to exactly represent the geometry by means of the usual CAD description of the boundary with non‐uniform rational B‐splines (NURBS...

high‐order isoparametric finite elements | CAD | transient Maxwell equations | discontinuous Galerkin | exact geometry representation | finite elements | NURBS | Discontinuous Galerkin | Finite elements | Transient Maxwell equations | High-order isoparametric finite elements | Exact geometry representation | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mathematics | Science & Technology | Corbes algebraiques | Geometria | Splines (Matemàtica) | Matemàtiques i estadística | Curves, Algebraic | Spline theory | Àrees temàtiques de la UPC | Geometria algebraica

high‐order isoparametric finite elements | CAD | transient Maxwell equations | discontinuous Galerkin | exact geometry representation | finite elements | NURBS | Discontinuous Galerkin | Finite elements | Transient Maxwell equations | High-order isoparametric finite elements | Exact geometry representation | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mathematics | Science & Technology | Corbes algebraiques | Geometria | Splines (Matemàtica) | Matemàtiques i estadística | Curves, Algebraic | Spline theory | Àrees temàtiques de la UPC | Geometria algebraica

Journal Article

2019, SpringerBriefs in mathematics, ISBN 303027229X, 131

This monograph requires basic knowledge of the variational theory of elliptic PDE and the techniques used for the analysis of the Finite Element Method...

Finite element method | Galerkin methods

Finite element method | Galerkin methods

eBook

Computer methods in applied mechanics and engineering, ISSN 0045-7825, 10/2012, Volume 241-244, pp. 225 - 237

► We present a meshfree Petrov–Galerkin method for 2-D convection–diffusion problems. ► The basis functions are determined via a local maximum-entropy optimisation process...

Petrov–Galerkin method | Information-flux method | Green’s function | Meshfree methods | Convection–diffusion problem | Maximum-entropy | Green's function | Convection-diffusion problem | Petrov-Galerkin method | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mechanics | Mathematics | Science & Technology | Finite element method | Methods | Stability | Approximation | Basis functions | Mathematical analysis | Meshless methods | Mathematical models | Weighting functions

Petrov–Galerkin method | Information-flux method | Green’s function | Meshfree methods | Convection–diffusion problem | Maximum-entropy | Green's function | Convection-diffusion problem | Petrov-Galerkin method | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mechanics | Mathematics | Science & Technology | Finite element method | Methods | Stability | Approximation | Basis functions | Mathematical analysis | Meshless methods | Mathematical models | Weighting functions

Journal Article

Computer methods in applied mechanics and engineering, ISSN 0045-7825, 04/2018, Volume 332, pp. 303 - 324

We introduce a family of Galerkin finite element methods which are constructed via recovery operators over element-wise discontinuous approximation spaces...

A priori error analysis | Finite element method | Discontinuous Galerkin | Conforming recovery operator | A posteriori error bound | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mechanics | Mathematics | Science & Technology | Analysis | Methods | Operators | Boundary value problems | Approximation | Partial differential equations | Mathematical analysis | Galerkin method | Finite element analysis | Recovery | Mathematics - Numerical Analysis

A priori error analysis | Finite element method | Discontinuous Galerkin | Conforming recovery operator | A posteriori error bound | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mechanics | Mathematics | Science & Technology | Analysis | Methods | Operators | Boundary value problems | Approximation | Partial differential equations | Mathematical analysis | Galerkin method | Finite element analysis | Recovery | Mathematics - Numerical Analysis

Journal Article

Computer methods in applied mechanics and engineering, ISSN 0045-7825, 08/2018, Volume 338, pp. 533 - 561

This paper marks the debut of a Galerkin isogeometric method for solving a Fredholm integral eigenvalue problem, enabling random field discretization by means of the Karhunen–Loève expansion...

Uncertainty quantification | Hilbert–Schmidt operator | Fredholm integral eigenvalue problem | B-splines | NURBS | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mechanics | Mathematics | Science & Technology | Uncertainty | Stress analysis | Basis functions | Computer simulation | Splines | Stochastic processes | Approximations | Subspace methods | Finite element method | Discretization | Computation | Mathematical analysis | Meshless methods | Eigenvalues | Hilbert space | Mathematical models | Galerkin method | Fields (mathematics) | Eigen values

Uncertainty quantification | Hilbert–Schmidt operator | Fredholm integral eigenvalue problem | B-splines | NURBS | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mechanics | Mathematics | Science & Technology | Uncertainty | Stress analysis | Basis functions | Computer simulation | Splines | Stochastic processes | Approximations | Subspace methods | Finite element method | Discretization | Computation | Mathematical analysis | Meshless methods | Eigenvalues | Hilbert space | Mathematical models | Galerkin method | Fields (mathematics) | Eigen values

Journal Article

IEEE transactions on antennas and propagation, ISSN 0018-926X, 01/2015, Volume 63, Issue 1, pp. 195 - 209

...-dimensional integrals over triangle-product domains, such as those arising in the boundary-element method (BEM...

Boundary-element method (BEM) | Closed-form solutions | Time division multiplexing | method of moments (MOM) | Galerkin formulation | Open source software | electric-field integral equation (EFIE) | magnetic-field integral equation (MFIE) | impedance matrix | code generation | Integral equations | computer algebra | singularity cancellation | singularity subtraction | Polynomials | singular integrals | Kernel | PMCHW | Engineering, Electrical & Electronic | Engineering | Telecommunications | Technology | Science & Technology | Finite element method | Usage | Numerical analysis | Electric fields | Innovations | Integrals | Finite element analysis | Algorithms | Mathematical analysis | Exact solutions | Mathematical models | Source code | Boundary element method | Computer programs

Boundary-element method (BEM) | Closed-form solutions | Time division multiplexing | method of moments (MOM) | Galerkin formulation | Open source software | electric-field integral equation (EFIE) | magnetic-field integral equation (MFIE) | impedance matrix | code generation | Integral equations | computer algebra | singularity cancellation | singularity subtraction | Polynomials | singular integrals | Kernel | PMCHW | Engineering, Electrical & Electronic | Engineering | Telecommunications | Technology | Science & Technology | Finite element method | Usage | Numerical analysis | Electric fields | Innovations | Integrals | Finite element analysis | Algorithms | Mathematical analysis | Exact solutions | Mathematical models | Source code | Boundary element method | Computer programs

Journal Article

Journal of computational physics, ISSN 0021-9991, 07/2017, Volume 341, pp. 341 - 376

...) method for the solution of the two and three dimensional compressible Euler and Navier...

All Mach number flows | Pressure-based semi-implicit space–time discontinuous Galerkin scheme | Compressible Navier–Stokes equations | Staggered unstructured meshes | High order of accuracy in space and time | Physical Sciences | Computer Science, Interdisciplinary Applications | Technology | Physics, Mathematical | Computer Science | Physics | Science & Technology | Fluid dynamics | Energy conservation | Statistics | Methods | Force and energy | Compressibility | Enthalpy | Fluid flow | Eulers equations | Finite volume method | Velocity distribution | High Mach number | Heat flux | Operators (mathematics) | Thermodynamics | Discretization | Mathematical analysis | Polynomials | Kinetic energy | Mach number | Conservation equations | Computer simulation | Preprocessing | Computational fluid dynamics | Numerical methods | Navier Stokes equations | Studies | Incompressible flow | Shock waves | Equations of state | Galerkin method | Kinetics | Heat transfer | Navier-Stokes equations | Mathematics - Numerical Analysis

All Mach number flows | Pressure-based semi-implicit space–time discontinuous Galerkin scheme | Compressible Navier–Stokes equations | Staggered unstructured meshes | High order of accuracy in space and time | Physical Sciences | Computer Science, Interdisciplinary Applications | Technology | Physics, Mathematical | Computer Science | Physics | Science & Technology | Fluid dynamics | Energy conservation | Statistics | Methods | Force and energy | Compressibility | Enthalpy | Fluid flow | Eulers equations | Finite volume method | Velocity distribution | High Mach number | Heat flux | Operators (mathematics) | Thermodynamics | Discretization | Mathematical analysis | Polynomials | Kinetic energy | Mach number | Conservation equations | Computer simulation | Preprocessing | Computational fluid dynamics | Numerical methods | Navier Stokes equations | Studies | Incompressible flow | Shock waves | Equations of state | Galerkin method | Kinetics | Heat transfer | Navier-Stokes equations | Mathematics - Numerical Analysis

Journal Article

Mathematics of computation, ISSN 0025-5718, 04/2014, Volume 83, Issue 286, pp. 537 - 552

We give a complete error analysis of the Discontinuous Petrov Galerkin (DPG) method, accounting for all the approximations made in its practical implementation...

DPG method | Petrov-Galerkin | Ultraweak formulation | Discontinuous galerkin | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

DPG method | Petrov-Galerkin | Ultraweak formulation | Discontinuous galerkin | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Journal of computational and applied mathematics, ISSN 0377-0427, 03/2013, Volume 241, Issue 1, pp. 103 - 115

This paper introduces a finite element method by using a weakly defined gradient operator over generalized functions...

Mixed finite element methods | Galerkin finite element methods | Second-order elliptic problems | Discrete gradient | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Finite element method | Analysis | Methods | Operators | Approximation | Mathematical analysis | Norms | Mathematical models | Galerkin methods | Optimization

Mixed finite element methods | Galerkin finite element methods | Second-order elliptic problems | Discrete gradient | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Finite element method | Analysis | Methods | Operators | Approximation | Mathematical analysis | Norms | Mathematical models | Galerkin methods | Optimization

Journal Article

Journal of computational and applied mathematics, ISSN 0377-0427, 09/2015, Volume 285, pp. 45 - 58

The weak Galerkin (WG) is a novel numerical method based on variational principles for weak functions and their weak partial derivatives defined as distributions...

Second-order elliptic equation | Discrete weak gradient | Weak Galerkin | Finite element methods | Weak gradient | Polyhedral meshes | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Finite element method | Analysis | Methods |

Second-order elliptic equation | Discrete weak gradient | Weak Galerkin | Finite element methods | Weak gradient | Polyhedral meshes | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Finite element method | Analysis | Methods |