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POD-Galerkin method for finite volume approximation of Navier–Stokes and RANS equations

Computer methods in applied mechanics and engineering, ISSN 0045-7825, 2016, Volume 311, pp. 151 - 179

.... In this work, the efforts have been put to develop a ROM for Computational Fluid Dynamics (CFD) application based on Finite Volume approximation, starting from the results available in turbulent Reynold-Averaged Navier...

Parametrized Navier–Stokes Equation | Proper orthogonal decomposition | Reduced order modelling | RANS | Galerkin projection | REPRESENTATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EDDY-VISCOSITY | EVOLUTION | ENGINEERING, MULTIDISCIPLINARY | MODELS | CLOSED-LOOP CONTROL | DYNAMICS | Parametrized Navier-Stokes Equation | TURBULENCE | FLOWS | COHERENT STRUCTURES | Numerical analysis | Fluid dynamics | Analysis | Methods | Force and energy

Parametrized Navier–Stokes Equation | Proper orthogonal decomposition | Reduced order modelling | RANS | Galerkin projection | REPRESENTATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EDDY-VISCOSITY | EVOLUTION | ENGINEERING, MULTIDISCIPLINARY | MODELS | CLOSED-LOOP CONTROL | DYNAMICS | Parametrized Navier-Stokes Equation | TURBULENCE | FLOWS | COHERENT STRUCTURES | Numerical analysis | Fluid dynamics | Analysis | Methods | Force and energy

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2004, Volume 298, Issue 1, pp. 279 - 291

Viscosity approximation methods for nonexpansive mappings are studied. Consider a nonexpansive self-mapping T of a closed convex subset C of a Banach space X...

Viscosity approximation | Nonexpansive mapping | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED | fixed point | BANACH-SPACES | nonexpansive mapping | CONVERGENCE | viscosity approximation | FIXED-POINTS

Viscosity approximation | Nonexpansive mapping | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED | fixed point | BANACH-SPACES | nonexpansive mapping | CONVERGENCE | viscosity approximation | FIXED-POINTS

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2014, Volume 52, Issue 2, pp. 993 - 1016

We propose an hp-version discontinuous Galerkin finite element method for fully nonlinear second-order elliptic Hamilton–Jacobi...

Ellipticity | Approximation | Mathematical discontinuity | Mathematical monotonicity | Fens | Polynomials | Coefficients | Newtons method | Stencils | Degrees of polynomials | Semismooth Newton methods | Fully nonlinear equations | Hamilton-Jacobi-Bellman equations | Cordes condition | Hp-version discontinuous Galerkin finite element methods | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | PARABOLIC EQUATIONS | fully nonlinear equations | semismooth Newton methods | CONVERGENT DIFFERENCE-SCHEMES | ELLIPTIC-EQUATIONS | hp-version discontinuous Galerkin finite element methods | Finite element method | Rope | Mathematical analysis | Nonlinearity | Mathematical models | Computational efficiency | Galerkin methods

Ellipticity | Approximation | Mathematical discontinuity | Mathematical monotonicity | Fens | Polynomials | Coefficients | Newtons method | Stencils | Degrees of polynomials | Semismooth Newton methods | Fully nonlinear equations | Hamilton-Jacobi-Bellman equations | Cordes condition | Hp-version discontinuous Galerkin finite element methods | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | PARABOLIC EQUATIONS | fully nonlinear equations | semismooth Newton methods | CONVERGENT DIFFERENCE-SCHEMES | ELLIPTIC-EQUATIONS | hp-version discontinuous Galerkin finite element methods | Finite element method | Rope | Mathematical analysis | Nonlinearity | Mathematical models | Computational efficiency | Galerkin methods

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 03/2018, Volume 86, Issue 8, pp. 541 - 563

.... The main advantage of this approach is that the mass matrix is time‐independent making this technique suitable for spectral methods...

level set method | incompressible flows | finite elements | multiphase flows | magnetohydrodynamics | pseudo‐spectral methods | pseudo-spectral methods | INSTABILITY | PHYSICS, FLUIDS & PLASMAS | LIQUID | EQUATIONS | MODEL | VARIABLE-DENSITY | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PROJECTION METHOD | REDUCTION CELLS | SIMULATIONS | Fluid dynamics | Viscosity | Industrial production | Compression | Methodology | Aluminum | Fluid flow | Maxwell's equations | Entropy | Spectral methods | Fluids | Solutions | Mathematical models | Mass matrix | Approximation | Computer simulation | Computational fluid dynamics | Momentum | Aluminium | Equations | Incompressible flow | Numerical analysis | Dependent variables | Multiphase | Conducting fluids | Surface tension | Navier-Stokes equations

level set method | incompressible flows | finite elements | multiphase flows | magnetohydrodynamics | pseudo‐spectral methods | pseudo-spectral methods | INSTABILITY | PHYSICS, FLUIDS & PLASMAS | LIQUID | EQUATIONS | MODEL | VARIABLE-DENSITY | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PROJECTION METHOD | REDUCTION CELLS | SIMULATIONS | Fluid dynamics | Viscosity | Industrial production | Compression | Methodology | Aluminum | Fluid flow | Maxwell's equations | Entropy | Spectral methods | Fluids | Solutions | Mathematical models | Mass matrix | Approximation | Computer simulation | Computational fluid dynamics | Momentum | Aluminium | Equations | Incompressible flow | Numerical analysis | Dependent variables | Multiphase | Conducting fluids | Surface tension | Navier-Stokes equations

Journal Article

Mathematical methods in the applied sciences, ISSN 1099-1476, 2018, Volume 42, Issue 1, pp. 250 - 271

.... The method is based on the convergence study of a sequence towards the solution, for which the rates are also given...

global existence result | low‐Mach model | convergence rates | low-Mach model | EXISTENCE | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | NUMBER LIMIT | COMPRESSIBLE FLOWS | SYSTEMS | INCOMPRESSIBLE LIMIT | WELL-POSEDNESS | Viscosity | Iterative methods | Temperature dependence | Numerical Analysis | Analysis of PDEs | Mathematics

global existence result | low‐Mach model | convergence rates | low-Mach model | EXISTENCE | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | NUMBER LIMIT | COMPRESSIBLE FLOWS | SYSTEMS | INCOMPRESSIBLE LIMIT | WELL-POSEDNESS | Viscosity | Iterative methods | Temperature dependence | Numerical Analysis | Analysis of PDEs | Mathematics

Journal Article

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, ISSN 0035-8711, 10/2019, Volume 488, Issue 4, pp. 5290 - 5299

Motivated by the stability of dust laden vortices, in this paper we study the terminal velocity approximation equations for a gas coupled to a pressureless dust fluid and present a numerical solver...

PROFILES | protoplanetary discs | PARTICLES | ALGORITHM | hydrodynamics | VISCOSITY | methods: numerical | GRAINS | ASTRONOMY & ASTROPHYSICS | methods: analytical | GAS | SYSTEMS | NUMERICAL SIMULATIONS | shock waves

PROFILES | protoplanetary discs | PARTICLES | ALGORITHM | hydrodynamics | VISCOSITY | methods: numerical | GRAINS | ASTRONOMY & ASTROPHYSICS | methods: analytical | GAS | SYSTEMS | NUMERICAL SIMULATIONS | shock waves

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 11/2008, Volume 53, Issue 10, pp. 2335 - 2350

.... Both methods provide analytical approximations of the stable Lagrangian submanifold from which the stabilizing solution is derived. Two examples illustrate the effectiveness of the methods.

Nonlinear equations | Hamilton-Jacobi equation | Partial differential equations | Control systems | Feedback control | Approximation methods | nonlinear control theory | symplectic geometry | perturbation method | Geometry | Hamiltonian systems | Perturbation methods | Riccati equations | Optimal control | stable manifold theory | Control theory | VISCOSITY SOLUTIONS | DESIGN | NONLINEAR-SYSTEMS | DYNAMICAL-SYSTEMS | H-INFINITY-CONTROL | INNER-OUTER FACTORIZATION | FEEDBACK | GEOMETRY | Perturbation method | Nonlinear control theory | Symplectic geometry | Stable manifold theory | ENGINEERING, ELECTRICAL & ELECTRONIC | AUTOMATION & CONTROL SYSTEMS | Evaluation | Perturbation (Mathematics) | Approximation theory | Matrices | Design and construction | Research | Methods

Nonlinear equations | Hamilton-Jacobi equation | Partial differential equations | Control systems | Feedback control | Approximation methods | nonlinear control theory | symplectic geometry | perturbation method | Geometry | Hamiltonian systems | Perturbation methods | Riccati equations | Optimal control | stable manifold theory | Control theory | VISCOSITY SOLUTIONS | DESIGN | NONLINEAR-SYSTEMS | DYNAMICAL-SYSTEMS | H-INFINITY-CONTROL | INNER-OUTER FACTORIZATION | FEEDBACK | GEOMETRY | Perturbation method | Nonlinear control theory | Symplectic geometry | Stable manifold theory | ENGINEERING, ELECTRICAL & ELECTRONIC | AUTOMATION & CONTROL SYSTEMS | Evaluation | Perturbation (Mathematics) | Approximation theory | Matrices | Design and construction | Research | Methods

Journal Article

Mathematics of computation, ISSN 1088-6842, 2018, Volume 88, Issue 315, pp. 273 - 291

We consider a finite-difference semi-discrete scheme for the approximation of boundary controls for the one-dimensional wave equation...

Wave equation | Moment problem | Biorthogonal families | Control approximation | moment problem | MATHEMATICS, APPLIED | control approximation | VANISHING VISCOSITY | biorthogonal families | 1-D | SYSTEMS | CONTROLLABILITY | Analysis of PDEs | Mathematics | Optimization and Control

Wave equation | Moment problem | Biorthogonal families | Control approximation | moment problem | MATHEMATICS, APPLIED | control approximation | VANISHING VISCOSITY | biorthogonal families | 1-D | SYSTEMS | CONTROLLABILITY | Analysis of PDEs | Mathematics | Optimization and Control

Journal Article

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General viscosity approximation methods for quasi-nonexpansive mappings with applications

Journal of inequalities and applications, ISSN 1029-242X, 2019, Volume 2019, Issue 1, pp. 1 - 20

The purpose of this paper is to introduce and study the general viscosity approximation methods for quasi-nonexpansive mappings in the setting of infinite-dimensional Hilbert spaces...

Split equality fixed point problems | Analysis | Quasi-nonexpansive mappings | Split equality null point problems | Viscosity approximation methods | 47H09 | Mathematics, general | Mathematics | Applications of Mathematics | 47J25 | Variational inequalities | MATHEMATICS | MATHEMATICS, APPLIED | MONOTONE | VARIATIONAL INEQUALITY | ITERATIVE ALGORITHMS | OPERATORS | FIXED-POINT PROBLEMS | Viscosity | Operation support systems | Algorithms | Approximation | Mathematical analysis | Hilbert space | Equality

Split equality fixed point problems | Analysis | Quasi-nonexpansive mappings | Split equality null point problems | Viscosity approximation methods | 47H09 | Mathematics, general | Mathematics | Applications of Mathematics | 47J25 | Variational inequalities | MATHEMATICS | MATHEMATICS, APPLIED | MONOTONE | VARIATIONAL INEQUALITY | ITERATIVE ALGORITHMS | OPERATORS | FIXED-POINT PROBLEMS | Viscosity | Operation support systems | Algorithms | Approximation | Mathematical analysis | Hilbert space | Equality

Journal Article

Annales de l'Institut Henri Poincaré. Analyse non linéaire, ISSN 0294-1449, 2019, Volume 36, Issue 1, pp. 53 - 74

In this paper, we propose an approximation method to study the regularity of solutions to the Isaacs equation...

Regularity theory | Isaacs equations | Approximation methods | Estimates in Sobolev and Hölder spaces | EXISTENCE | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | Estimates in Sobolev and Holder spaces | INTERIOR | DIFFERENTIAL-GAMES | ELLIPTIC-EQUATIONS | FULLY NONLINEAR EQUATIONS

Regularity theory | Isaacs equations | Approximation methods | Estimates in Sobolev and Hölder spaces | EXISTENCE | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | Estimates in Sobolev and Holder spaces | INTERIOR | DIFFERENTIAL-GAMES | ELLIPTIC-EQUATIONS | FULLY NONLINEAR EQUATIONS

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2016, Volume 2016, Issue 1, pp. 1 - 12

In this paper, we study viscosity approximations with ( ψ , φ ) $(\psi,\varphi)$ -weakly contractive mappings...

Halpern type convergence | Mathematical and Computational Biology | ( ψ , φ ) $(\psi,\varphi)$ -weakly contractive mappings | Moudafi’s viscosity approximations | Mathematics | Topology | 54H25 | 47H10 | Browder type convergence | Analysis | Mathematics, general | Applications of Mathematics | Differential Geometry | (ψ, φ) -weakly contractive mappings | Viscosity | Theorems | Approximation | Texts | Mapping | Approximation methods | Formulas (mathematics) | Convergence

Halpern type convergence | Mathematical and Computational Biology | ( ψ , φ ) $(\psi,\varphi)$ -weakly contractive mappings | Moudafi’s viscosity approximations | Mathematics | Topology | 54H25 | 47H10 | Browder type convergence | Analysis | Mathematics, general | Applications of Mathematics | Differential Geometry | (ψ, φ) -weakly contractive mappings | Viscosity | Theorems | Approximation | Texts | Mapping | Approximation methods | Formulas (mathematics) | Convergence

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 2013, Volume 2013, Issue 1

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2014, Volume 2014, Issue 1, pp. 1 - 11

We combine a sequence of contractive mappings and propose a generalized viscosity approximation method...

Mathematical and Computational Biology | fixed point | Analysis | viscosity approximation method | contractive mapping | Mathematics, general | nonexpansive mapping | Mathematics | variational inequality | Applications of Mathematics | Topology | Differential Geometry | Contractive mapping | Variational inequality | Viscosity approximation method | Nonexpansive mapping | Fixed point | MATHEMATICS | FAMILIES | STRONG-CONVERGENCE THEOREMS | FIXED-POINTS | Fixed point theory | Usage | Approximation theory | Distributions, Theory of (Functional analysis) | Contraction operators | Viscosity | Approximation | Mathematical analysis | Inequalities | Hilbert space | Mapping | Iterative methods | Convergence

Mathematical and Computational Biology | fixed point | Analysis | viscosity approximation method | contractive mapping | Mathematics, general | nonexpansive mapping | Mathematics | variational inequality | Applications of Mathematics | Topology | Differential Geometry | Contractive mapping | Variational inequality | Viscosity approximation method | Nonexpansive mapping | Fixed point | MATHEMATICS | FAMILIES | STRONG-CONVERGENCE THEOREMS | FIXED-POINTS | Fixed point theory | Usage | Approximation theory | Distributions, Theory of (Functional analysis) | Contraction operators | Viscosity | Approximation | Mathematical analysis | Inequalities | Hilbert space | Mapping | Iterative methods | Convergence

Journal Article

Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, ISSN 0308-2105, 08/2018, Volume 148, Issue 4, pp. 819 - 834

In this paper we show that conforming Galerkin approximations for p-harmonic functions tend...

Galerkin methods | Laplacian | viscosity solutions | Harmonic functions | Galerkin method

Galerkin methods | Laplacian | viscosity solutions | Harmonic functions | Galerkin method

Journal Article

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Viscosity approximation methods for asymptotically nonexpansive mapping in CAT(0) spaces

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2015, Volume 2015, Issue 1, pp. 1 - 15

...Wangkeeree et al. Fixed Point Theory and Applications null2015)null015:23null DOI 10.1186/s13663-015-0273-x R E S E A R C H Open Access Viscosity approximation...

Mathematical and Computational Biology | Analysis | viscosity approximation method | CAT space | common fixed point | Mathematics, general | Mathematics | variational inequality | Applications of Mathematics | Topology | Differential Geometry | asymptotically nonexpansive mapping | MATHEMATICS | SEMIGROUPS | CONVERGENCE THEOREMS | FIXED-POINTS | Viscosity | Fixed point theory | Approximation theory | Methods | Theorems | Approximation | Asymptotic properties | Mathematical analysis | Inequalities | Mapping | Convergence

Mathematical and Computational Biology | Analysis | viscosity approximation method | CAT space | common fixed point | Mathematics, general | Mathematics | variational inequality | Applications of Mathematics | Topology | Differential Geometry | asymptotically nonexpansive mapping | MATHEMATICS | SEMIGROUPS | CONVERGENCE THEOREMS | FIXED-POINTS | Viscosity | Fixed point theory | Approximation theory | Methods | Theorems | Approximation | Asymptotic properties | Mathematical analysis | Inequalities | Mapping | Convergence

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 10/2016, Volume 13, Issue 5, pp. 2645 - 2657

Based on some iteration schemes, we study the viscosity approximation results for multivalued nonexpansive mappings in Hilbert space and Banach space...

Secondary 49J40 | Multivalued nonexpansive mapping | 47H09 | Mathematics, general | Mathematics | variational inequality | fixed-point theorems | Primary 47H10 | MATHEMATICS, APPLIED | CONTRACTION-MAPPINGS | METRIC-SPACES | MULTIFUNCTIONS | MATHEMATICS | BANACH-SPACES | ISHIKAWA ITERATION | MANN | FIXED-POINT | CONVERGENCE

Secondary 49J40 | Multivalued nonexpansive mapping | 47H09 | Mathematics, general | Mathematics | variational inequality | fixed-point theorems | Primary 47H10 | MATHEMATICS, APPLIED | CONTRACTION-MAPPINGS | METRIC-SPACES | MULTIFUNCTIONS | MATHEMATICS | BANACH-SPACES | ISHIKAWA ITERATION | MANN | FIXED-POINT | CONVERGENCE

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2006, Volume 321, Issue 1, pp. 316 - 326

.... Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. 298 (2004) 279–291].

Nonexpansive nonself-mappings | Viscosity approximation | Weakly sequentially continuous duality mapping | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED | nonexpansive nonself-mappings | fixed point | BANACH-SPACES | weakly sequentially continuous duality mapping | CONVERGENCE | viscosity approximation | FIXED-POINTS

Nonexpansive nonself-mappings | Viscosity approximation | Weakly sequentially continuous duality mapping | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED | nonexpansive nonself-mappings | fixed point | BANACH-SPACES | weakly sequentially continuous duality mapping | CONVERGENCE | viscosity approximation | FIXED-POINTS

Journal Article

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Viscosity approximation methods for multivalued nonexpansive mappings in geodesic spaces

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2015, Volume 2015, Issue 1, pp. 1 - 14

We prove strong convergence of the viscosity approximation method for multivalued nonexpansive mappings in CAT ( 0 ) $\operatorname{CAT}(0)$ spaces...

Mathematical and Computational Biology | fixed point | Analysis | viscosity approximation method | CAT $\operatorname{CAT}$ space | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | multivalued nonexpansive mapping | strong convergence | CAT space | CONVERGENCE THEOREM | MATHEMATICS | MATHEMATICS, APPLIED | TREES | BANACH-SPACES | CAT SPACES | FIXED-POINTS | Usage | Approximation theory | Convergence (Mathematics) | Viscosity | Texts | Mapping | Approximation | Mathematical analysis | Convergence

Mathematical and Computational Biology | fixed point | Analysis | viscosity approximation method | CAT $\operatorname{CAT}$ space | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | multivalued nonexpansive mapping | strong convergence | CAT space | CONVERGENCE THEOREM | MATHEMATICS | MATHEMATICS, APPLIED | TREES | BANACH-SPACES | CAT SPACES | FIXED-POINTS | Usage | Approximation theory | Convergence (Mathematics) | Viscosity | Texts | Mapping | Approximation | Mathematical analysis | Convergence

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2006, Volume 318, Issue 1, pp. 43 - 52

... {xn} generated by the iterative method xn+1=(I−αnA)Txn+αnγf(xn) converges strongly to a fixed point x˜∈Fix...

Iterative method | Projection | Variational inequality | Nonexpansive mapping | Viscosity approximation | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED |

Iterative method | Projection | Variational inequality | Nonexpansive mapping | Viscosity approximation | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED |