Journal of Computational Physics, ISSN 0021-9991, 02/2016, Volume 307, pp. 401 - 422

... by either convection or diffusion. Subsequently, the linear advection equation augmented with spectral vanishing viscosity (SVV) is analysed...

Dispersion–diffusion analysis | Stabilization for DNS/LES | Spectral vanishing viscosity | Continuous Galerkin formulation | Dispersion-diffusion analysis | NONLINEAR CONSERVATION-LAWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DISPERSION | LARGE-EDDY SIMULATIONS | FLOWS | PHYSICS, MATHEMATICAL | TURBULENCE SIMULATIONS | Mathematical optimization | Analysis | Peclet number | Kernel functions | Mathematical analysis | Dissipation | Spectra | Diffusion | Galerkin methods | Dispersion

Dispersion–diffusion analysis | Stabilization for DNS/LES | Spectral vanishing viscosity | Continuous Galerkin formulation | Dispersion-diffusion analysis | NONLINEAR CONSERVATION-LAWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DISPERSION | LARGE-EDDY SIMULATIONS | FLOWS | PHYSICS, MATHEMATICAL | TURBULENCE SIMULATIONS | Mathematical optimization | Analysis | Peclet number | Kernel functions | Mathematical analysis | Dissipation | Spectra | Diffusion | Galerkin methods | Dispersion

Journal Article

Physica. D, ISSN 0167-2789, 2018, Volume 376-377, pp. 238 - 246

In this paper, we are concerned with the vanishing viscosity problem for the three-dimensional Navier...

Navier–Stokes equations | Vanishing viscosity limit | Euler equations | Helical symmetry | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | PHYSICS, MULTIDISCIPLINARY | REGULARITY | 3-DIMENSIONAL EULER EQUATIONS | WEAK SOLUTIONS | PHYSICS, MATHEMATICAL | Navier-Stokes equations | Mathematics - Analysis of PDEs

Navier–Stokes equations | Vanishing viscosity limit | Euler equations | Helical symmetry | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | PHYSICS, MULTIDISCIPLINARY | REGULARITY | 3-DIMENSIONAL EULER EQUATIONS | WEAK SOLUTIONS | PHYSICS, MATHEMATICAL | Navier-Stokes equations | Mathematics - Analysis of PDEs

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 08/2018, Volume 376-377, pp. 31 - 38

.... We show that the damped Euler system has a (strong) global attractor in H1(Ω). We also show that in the vanishing viscosity limit the global attractors of the Navier...

Vanishing viscosity limit | Damped Euler equations | Global attractors | EXISTENCE | MATHEMATICS, APPLIED | TRAJECTORY ATTRACTORS | PHYSICS, MULTIDISCIPLINARY | SPATIALLY NONDECAYING SOLUTIONS | EQUATIONS | PHYSICS, MATHEMATICAL | UNIQUENESS | SEMIGROUPS | DISSIPATIVE 2D EULER | R-2 | DOMAINS | STRONG-CONVERGENCE | Mathematics - Analysis of PDEs

Vanishing viscosity limit | Damped Euler equations | Global attractors | EXISTENCE | MATHEMATICS, APPLIED | TRAJECTORY ATTRACTORS | PHYSICS, MULTIDISCIPLINARY | SPATIALLY NONDECAYING SOLUTIONS | EQUATIONS | PHYSICS, MATHEMATICAL | UNIQUENESS | SEMIGROUPS | DISSIPATIVE 2D EULER | R-2 | DOMAINS | STRONG-CONVERGENCE | Mathematics - Analysis of PDEs

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 06/2019, Volume 266, Issue 12, pp. 8110 - 8163

.... We focus on the one dimensional (planar) version of the model and address the problem of well posedness as well as convergence of the sequence of solutions as the bulk viscosity tends to zero together with some other interaction parameters...

Compressible MHD planar equations | Vanishing viscosity | Nonlinear Schrödinger equation | MATHEMATICS | Nonlinear Schrodinger equation | ISENTROPIC GAS-DYNAMICS | CONVERGENCE | SYSTEMS | EULER EQUATIONS

Compressible MHD planar equations | Vanishing viscosity | Nonlinear Schrödinger equation | MATHEMATICS | Nonlinear Schrodinger equation | ISENTROPIC GAS-DYNAMICS | CONVERGENCE | SYSTEMS | EULER EQUATIONS

Journal Article

5.
Full Text
Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity

Mathematical programming, ISSN 1436-4646, 2016, Volume 168, Issue 1-2, pp. 123 - 175

... with asymptotic vanishing viscosity Hedy Attouch 1 · Zaki Chbani 2 · Juan Peypouquet 3 · Patrick Redont 1 Received: 22 August 2015 / Accepted: 7 February 2016 / Published...

65K05 | Inertial dynamics | Theoretical, Mathematical and Computational Physics | Mathematics | Gradient flows | Dynamical systems | 34D05 | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Fast convergent methods | Vanishing viscosity | 65K10 | Combinatorics | 49M25 | Nesterov method | SYSTEM | MATHEMATICS, APPLIED | MAXIMAL MONOTONE-OPERATORS | PROXIMAL METHOD | BEHAVIOR | EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Analysis | Algorithms | Differential equations | Hilbert space | Trajectories | Nonlinear programming | Convergence | Viscous damping | Optimization and Control

65K05 | Inertial dynamics | Theoretical, Mathematical and Computational Physics | Mathematics | Gradient flows | Dynamical systems | 34D05 | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Fast convergent methods | Vanishing viscosity | 65K10 | Combinatorics | 49M25 | Nesterov method | SYSTEM | MATHEMATICS, APPLIED | MAXIMAL MONOTONE-OPERATORS | PROXIMAL METHOD | BEHAVIOR | EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Analysis | Algorithms | Differential equations | Hilbert space | Trajectories | Nonlinear programming | Convergence | Viscous damping | Optimization and Control

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2017, Volume 369, Issue 3, pp. 2003 - 2027

Whether, in the presence of a boundary, solutions of the Navier-Stokes equations converge to a solution to the Euler equations in the vanishing viscosity limit is unknown...

Boundary layer theory | Vanishing viscosity | boundary layer theory | MATHEMATICS | NAVIER-STOKES EQUATIONS | APPROXIMATION | BOUNDARY-LAYERS | PLANE | FLOWS | VORTICITY | INVISCID LIMIT

Boundary layer theory | Vanishing viscosity | boundary layer theory | MATHEMATICS | NAVIER-STOKES EQUATIONS | APPROXIMATION | BOUNDARY-LAYERS | PLANE | FLOWS | VORTICITY | INVISCID LIMIT

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2019, Volume 266, Issue 1, pp. 312 - 351

... x. By adding a small viscosity, one obtains a well posed parabolic equation. As the viscous term goes to zero, the uniqueness of the vanishing viscosity limit is proved...

Conservation law with discontinuous flux | Regulated flux function | Hamilton–Jacobi equation | Existence and uniqueness | Vanishing viscosity | EXISTENCE | Hamilton-Jacobi equation | RESONANT SYSTEM | APPROXIMATION | ENTROPY CONDITIONS | EQUATIONS | CAUCHY-PROBLEM | UNIQUENESS | MATHEMATICS | DISCONTINUOUS FLUX | COEFFICIENTS | GRAVITATION | Environmental law

Conservation law with discontinuous flux | Regulated flux function | Hamilton–Jacobi equation | Existence and uniqueness | Vanishing viscosity | EXISTENCE | Hamilton-Jacobi equation | RESONANT SYSTEM | APPROXIMATION | ENTROPY CONDITIONS | EQUATIONS | CAUCHY-PROBLEM | UNIQUENESS | MATHEMATICS | DISCONTINUOUS FLUX | COEFFICIENTS | GRAVITATION | Environmental law

Journal Article

Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 04/2013, Volume 23, Issue 4, pp. 565 - 616

We analyze a rate-independent model for damage evolution in elastic bodies. The central quantities are a stored energy functional and a dissipation functional,...

Rate-independent damage evolution | vanishing viscosity method | arclength reparametrization | time discretization | EXISTENCE | MATHEMATICS, APPLIED | APPROXIMATION | SPACES | CRACK-PROPAGATION | EQUATIONS | NONLINEAR ELASTICITY | QUASI-STATIC EVOLUTION | SYSTEMS | FUNCTIONALS | PLASTICITY

Rate-independent damage evolution | vanishing viscosity method | arclength reparametrization | time discretization | EXISTENCE | MATHEMATICS, APPLIED | APPROXIMATION | SPACES | CRACK-PROPAGATION | EQUATIONS | NONLINEAR ELASTICITY | QUASI-STATIC EVOLUTION | SYSTEMS | FUNCTIONALS | PLASTICITY

Journal Article

SIAM journal on mathematical analysis, ISSN 1095-7154, 2019, Volume 51, Issue 3, pp. 2168 - 2205

We prove the convergence of the vanishing viscosity limit of the one-dimensional, isentropic, compressible Navier-Stokes equations to the isentropic Euler equations in the case of a general pressure law...

EXISTENCE | compensated compactness | MATHEMATICS, APPLIED | relative finite-energy | STABILITY | ISENTROPIC GAS-DYNAMICS | CONVERGENCE | vanishing viscosity | Euler equations | FLOW | Navier-Stokes equations | FRIEDRICHS SCHEME

EXISTENCE | compensated compactness | MATHEMATICS, APPLIED | relative finite-energy | STABILITY | ISENTROPIC GAS-DYNAMICS | CONVERGENCE | vanishing viscosity | Euler equations | FLOW | Navier-Stokes equations | FRIEDRICHS SCHEME

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 09/2017, Volume 40, Issue 14, pp. 5161 - 5176

...–Stokes equation is independent of viscosity, and that the solutions of the Navier–Stokes equation converge to that of Euler equation in Gevrey class as the viscosity tends to zero...

vanishing viscosity limit | incompressible Navier–Stokes equation | Gevrey class | incompressible Navier-Stokes equation | SYSTEM | MATHEMATICS, APPLIED | CLASS REGULARITY | WELL-POSEDNESS | ANALYTICITY | 3-DIMENSIONAL EULER EQUATIONS | HALF-SPACE | BOUNDARY | INITIAL DATA | PRANDTL EQUATION | Fluid dynamics | Viscosity | Life span | Fluid flow | Navier Stokes equations | Stokes law (fluid mechanics) | Navier-Stokes equations | Convergence | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

vanishing viscosity limit | incompressible Navier–Stokes equation | Gevrey class | incompressible Navier-Stokes equation | SYSTEM | MATHEMATICS, APPLIED | CLASS REGULARITY | WELL-POSEDNESS | ANALYTICITY | 3-DIMENSIONAL EULER EQUATIONS | HALF-SPACE | BOUNDARY | INITIAL DATA | PRANDTL EQUATION | Fluid dynamics | Viscosity | Life span | Fluid flow | Navier Stokes equations | Stokes law (fluid mechanics) | Navier-Stokes equations | Convergence | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 2006, Volume 203, Issue 2, pp. 497 - 513

In this paper, we prove the global in time regularity for the 2D Boussinesq system with either the zero diffusivity or the zero viscosity...

Vanishing viscosity limit | Boussinesq equations | Global regularity | Vanishing diffusivity limit | vanishing viscosity limit | MATHEMATICS | vanishing diffusivity limit | BLOW-UP CRITERION | global regularity | LOCAL EXISTENCE

Vanishing viscosity limit | Boussinesq equations | Global regularity | Vanishing diffusivity limit | vanishing viscosity limit | MATHEMATICS | vanishing diffusivity limit | BLOW-UP CRITERION | global regularity | LOCAL EXISTENCE

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 2/2019, Volume 78, Issue 2, pp. 1132 - 1151

In this work, we adapt techniques of artificial and spectral viscosities [especially those presented in Klöckner et al...

Discontinuous Galerkin | Computational Mathematics and Numerical Analysis | Algorithms | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Adaptive filtering | Mathematics | Artificial and spectral viscosity | MATHEMATICS, APPLIED | VANISHING VISCOSITY | IMPLEMENTATION | DISCONTINUOUS GALERKIN METHOD | HIGH-ORDER | SPACE | EDGE-DETECTION | TROUBLED-CELL INDICATORS | GIBBS PHENOMENON | LIMITERS | SCHEMES | Shock | Air bases | Analysis | Methods

Discontinuous Galerkin | Computational Mathematics and Numerical Analysis | Algorithms | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Adaptive filtering | Mathematics | Artificial and spectral viscosity | MATHEMATICS, APPLIED | VANISHING VISCOSITY | IMPLEMENTATION | DISCONTINUOUS GALERKIN METHOD | HIGH-ORDER | SPACE | EDGE-DETECTION | TROUBLED-CELL INDICATORS | GIBBS PHENOMENON | LIMITERS | SCHEMES | Shock | Air bases | Analysis | Methods

Journal Article

Nonlinearity, ISSN 0951-7715, 06/2015, Volume 28, Issue 6, pp. 1607 - 1631

This study considers the spatially periodic initial value problem of 2x2 quasi-linear parabolic systems in one space dimension having quadratic polynomial flux...

vanishing viscosity limit | high-order dissipation | mixed hyperbolic-elliptic systems | MATHEMATICS, APPLIED | WAVES | INSTABILITY | FLUID | REGIONS | EQUATIONS | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | Nonlinear dynamics | Multilayers | Mathematical analysis | Dissipation | Nonlinearity | Polynomials | Channel flow | Dynamical systems

vanishing viscosity limit | high-order dissipation | mixed hyperbolic-elliptic systems | MATHEMATICS, APPLIED | WAVES | INSTABILITY | FLUID | REGIONS | EQUATIONS | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | Nonlinear dynamics | Multilayers | Mathematical analysis | Dissipation | Nonlinearity | Polynomials | Channel flow | Dynamical systems

Journal Article

European journal of applied mathematics, ISSN 0956-7925, 02/2019, Volume 30, Issue 1, pp. 117 - 175

This article is the third one in a series of papers by the authors on vanishing-viscosity solutions to rate-independent damage systems...

Papers | Rate-independent damage system | Balanced Viscosity solutions | vanishing-viscosity approximation | MATHEMATICS, APPLIED | APPROXIMATION | EQUATIONS | BOUNDARY | LIMIT | MODEL | Viscosity | Knee | Boundary conditions | Parameterization | Damage

Papers | Rate-independent damage system | Balanced Viscosity solutions | vanishing-viscosity approximation | MATHEMATICS, APPLIED | APPROXIMATION | EQUATIONS | BOUNDARY | LIMIT | MODEL | Viscosity | Knee | Boundary conditions | Parameterization | Damage

Journal Article

ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 01/2012, Volume 18, Issue 1, pp. 36 - 80

.... To model such jumps, we adopt the philosophy that rate-independence should be considered as limit of systems with smaller and smaller viscosity...

Differential inclusions | Vanishing-viscosity contact potential | Vanishing-viscosity limit | Doubly nonlinear | Viscous regularization | Generalized gradient flows | Parameterized solutions | viscous regularization | EXISTENCE | MATHEMATICS, APPLIED | BEHAVIOR | LIMIT | MODEL | generalized gradient flows | FORMULATION | parameterized solutions | BRITTLE FRACTURES | QUASI-STATIC EVOLUTION | CRACK-GROWTH | vanishing-viscosity contact potential | differential inclusions | vanishing-viscosity limit | AUTOMATION & CONTROL SYSTEMS | PLASTICITY | Studies | Viscosity | Mathematical models | Mathematics | Calculus of variations | Mathematics - Analysis of PDEs

Differential inclusions | Vanishing-viscosity contact potential | Vanishing-viscosity limit | Doubly nonlinear | Viscous regularization | Generalized gradient flows | Parameterized solutions | viscous regularization | EXISTENCE | MATHEMATICS, APPLIED | BEHAVIOR | LIMIT | MODEL | generalized gradient flows | FORMULATION | parameterized solutions | BRITTLE FRACTURES | QUASI-STATIC EVOLUTION | CRACK-GROWTH | vanishing-viscosity contact potential | differential inclusions | vanishing-viscosity limit | AUTOMATION & CONTROL SYSTEMS | PLASTICITY | Studies | Viscosity | Mathematical models | Mathematics | Calculus of variations | Mathematics - Analysis of PDEs

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2016, Volume 18, Issue 9, pp. 2107 - 2165

J. Europ. Math. Soc. 18 (2016) 2107-2165 Balanced Viscosity solutions to rate-independent systems arise as limits of regularized rate-independent flows by adding a superlinear vanishing-viscosity dissipation...

Energetic solutions | Existence results | Time discretization | Rate-independent systems | BV solutions | Vanishing viscosity | Mathematics - Analysis of PDEs

Energetic solutions | Existence results | Time discretization | Rate-independent systems | BV solutions | Vanishing viscosity | Mathematics - Analysis of PDEs

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 05/2013, Volume 254, Issue 10, pp. 4122 - 4143

For a Hamilton–Jacobi equation defined on a network, we introduce its vanishing viscosity approximation...

Maximum principle | Hamilton–Jacobi equation | Viscosity solution | Vanishing viscosity | Network | Hamilton-Jacobi equation | MATHEMATICS | DIFFUSION-PROCESSES | PRINCIPLE | GRAPHS

Maximum principle | Hamilton–Jacobi equation | Viscosity solution | Vanishing viscosity | Network | Hamilton-Jacobi equation | MATHEMATICS | DIFFUSION-PROCESSES | PRINCIPLE | GRAPHS

Journal Article

Acta applicandae mathematicae, ISSN 1572-9036, 2017, Volume 153, Issue 1, pp. 101 - 124

...Acta Appl Math (2018) 153:101–124 DOI 10.1007/s10440-017-0122-5 L -Splines and Viscosity Limits for Well-Balanced Schemes Acting on Linear Parabolic Equations...

34D15 | Fundamental system of solutions | Theoretical, Mathematical and Computational Physics | Complex Systems | Monotone well-balanced scheme | 65M06 | Classical Mechanics | Mathematics | Constant/Line Perturbation method (C/L-PM) | Parabolic Cylinder functions (PCF) | 76R50 | 76M45 | Vanishing viscosity | Mathematics, general | Computer Science, general | ℒ-spline | MATHEMATICS, APPLIED | SINGULAR PERTURBATION PROBLEM | NUMERICAL-METHOD | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | WEAK VARIATIONAL FORMULATION | SOURCE TERMS | DISCRETIZATION | CYLINDER FUNCTIONS | SCALAR CONSERVATION-LAWS | DIFFUSION | L-spline | Viscosity | Boundary value problems | Kinetic equations | Splines | Asymptotic properties | Mathematical analysis | Numerical methods | Computational grids | Regularity | Finite difference method | Knots

34D15 | Fundamental system of solutions | Theoretical, Mathematical and Computational Physics | Complex Systems | Monotone well-balanced scheme | 65M06 | Classical Mechanics | Mathematics | Constant/Line Perturbation method (C/L-PM) | Parabolic Cylinder functions (PCF) | 76R50 | 76M45 | Vanishing viscosity | Mathematics, general | Computer Science, general | ℒ-spline | MATHEMATICS, APPLIED | SINGULAR PERTURBATION PROBLEM | NUMERICAL-METHOD | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | WEAK VARIATIONAL FORMULATION | SOURCE TERMS | DISCRETIZATION | CYLINDER FUNCTIONS | SCALAR CONSERVATION-LAWS | DIFFUSION | L-spline | Viscosity | Boundary value problems | Kinetic equations | Splines | Asymptotic properties | Mathematical analysis | Numerical methods | Computational grids | Regularity | Finite difference method | Knots

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 11/2019, Volume 277, Issue 10, pp. 3599 - 3652

.... In this paper we study the vanishing viscosity limit of sequences of these solutions. As the viscosity tends to zero, some sequences of solutions Clocm converge to solutions...

Stationary Navier-Stokes equations | Vanishing viscosity limit | Homogeneous axisymmetric no-swirl solutions | SIMILAR VISCOUS FLOWS | ANALYTIC SOLUTIONS | MATHEMATICS | ISOLATED SINGULARITIES | AXIAL CAUSES | HALF-SPACE | EULER | INVISCID LIMIT | Fluid dynamics

Stationary Navier-Stokes equations | Vanishing viscosity limit | Homogeneous axisymmetric no-swirl solutions | SIMILAR VISCOUS FLOWS | ANALYTIC SOLUTIONS | MATHEMATICS | ISOLATED SINGULARITIES | AXIAL CAUSES | HALF-SPACE | EULER | INVISCID LIMIT | Fluid dynamics

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2006, Volume 231, Issue 2, pp. 459 - 500

In this paper, using the vanishing viscosity method, we construct a solution of the Riemann problem for the system of conservation laws u t + ( u 2 ) x = 0 , v t + 2 ( u v ) x = 0 , w t + 2 ( v 2 + u w ) x...

δ-Shocks | [formula omitted]-Shocks | Vacuum states | Systems of conservation laws | Vanishing viscosity method | Weak asymptotics method | Shocks | HYPERBOLIC SYSTEMS | delta '-shocks | MATHEMATICS | PRESSURE LIMIT | WAVES | vanishing viscosity method | systems of conservation laws | delta-shocks | CONSERVATION-LAWS | weak asymptotics method | WEAK SOLUTIONS | EULER EQUATIONS | PROPAGATION | vacuum states

δ-Shocks | [formula omitted]-Shocks | Vacuum states | Systems of conservation laws | Vanishing viscosity method | Weak asymptotics method | Shocks | HYPERBOLIC SYSTEMS | delta '-shocks | MATHEMATICS | PRESSURE LIMIT | WAVES | vanishing viscosity method | systems of conservation laws | delta-shocks | CONSERVATION-LAWS | weak asymptotics method | WEAK SOLUTIONS | EULER EQUATIONS | PROPAGATION | vacuum states

Journal Article