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

...–Bellman equations with Cordes coefficients. The method is proved to be consistent and stable, with convergence rates that are optimal with respect to mesh size, and suboptimal in the polynomial degree by only half an order...

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

Journal of computational physics, ISSN 0021-9991, 2019, Volume 396, pp. 888 - 904

.... In the case of diffusion processes with piecewise constant coefficients, known as Skew Diffusions, such close form expressions for the resolvent...

Skew diffusions | Diffusion processes with discontinuous coefficients | Resolvent kernel | Monte Carlo | TIME | SIMULATION | PHYSICS, MATHEMATICAL | SCHEME | TRANSPORT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | POROUS-MEDIA | WALK PARTICLE TRACKING | NUMERICAL ASSESSMENT | Algorithms | Computer simulation | Diffusion | Exact solutions | Probability | Analysis of PDEs | Mathematics

Skew diffusions | Diffusion processes with discontinuous coefficients | Resolvent kernel | Monte Carlo | TIME | SIMULATION | PHYSICS, MATHEMATICAL | SCHEME | TRANSPORT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | POROUS-MEDIA | WALK PARTICLE TRACKING | NUMERICAL ASSESSMENT | Algorithms | Computer simulation | Diffusion | Exact solutions | Probability | Analysis of PDEs | Mathematics

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2015, Volume 259, Issue 11, pp. 5667 - 5687

We provide a higher differentiability result for the finite energy solutions u∈W1,1(Ω,RN) of a degenerate elliptic system of the formdivA(x,Du)=0inΩ⊂Rn, where...

Degenerate elliptic systems | Higher differentiability | Discontinuous coefficients | FINITE DISTORTION | EQUATIONS | QUASI-CONFORMAL MAPPINGS | MINIMIZERS | MATHEMATICS | CONVEX INTEGRALS | VARIATIONAL INTEGRALS | FUNCTIONALS | PARTIAL REGULARITY | GROWTH-CONDITIONS

Degenerate elliptic systems | Higher differentiability | Discontinuous coefficients | FINITE DISTORTION | EQUATIONS | QUASI-CONFORMAL MAPPINGS | MINIMIZERS | MATHEMATICS | CONVEX INTEGRALS | VARIATIONAL INTEGRALS | FUNCTIONALS | PARTIAL REGULARITY | GROWTH-CONDITIONS

Journal Article

Journal of computational physics, ISSN 0021-9991, 2018, Volume 362, pp. 20 - 48

High-order methods for conservation laws can be highly efficient if their stability is ensured. A suitable means mimicking estimates of the continuous level is...

Hyperbolic conservation laws | Skew-symmetric form | Stability | Summation-by-parts | Conservation | NONLINEAR CONSERVATION-LAWS | STRICT STABILITY | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATIONS | NUMERICAL APPROXIMATIONS | SPECTRAL ELEMENT DISCRETIZATION | FINITE-DIFFERENCE FORMULATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SPLIT-FORM | DISCRETE | DISCONTINUOUS GALERKIN METHODS | COLLOCATION SCHEMES | Environmental law | Analysis | Mathematics - Numerical Analysis

Hyperbolic conservation laws | Skew-symmetric form | Stability | Summation-by-parts | Conservation | NONLINEAR CONSERVATION-LAWS | STRICT STABILITY | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATIONS | NUMERICAL APPROXIMATIONS | SPECTRAL ELEMENT DISCRETIZATION | FINITE-DIFFERENCE FORMULATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SPLIT-FORM | DISCRETE | DISCONTINUOUS GALERKIN METHODS | COLLOCATION SCHEMES | Environmental law | Analysis | Mathematics - Numerical Analysis

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 04/2020, Volume 79, Issue 8, pp. 2336 - 2349

We present a new stabilization technique for multiscale convection–diffusion problems. Stabilization for these problems has been a challenging task, especially...

ROBUST DPG METHOD | MATHEMATICS, APPLIED | DOMAIN DECOMPOSITION PRECONDITIONERS | DISCONTINUOUS GALERKIN METHOD | FLOWS | FORMULATION | FINITE-ELEMENT-METHOD

ROBUST DPG METHOD | MATHEMATICS, APPLIED | DOMAIN DECOMPOSITION PRECONDITIONERS | DISCONTINUOUS GALERKIN METHOD | FLOWS | FORMULATION | FINITE-ELEMENT-METHOD

Journal Article

Water resources research, ISSN 0043-1397, 2011, Volume 47, Issue 10, p. n/a

...‐sided reflection coefficient that correctly represents the effect of discontinuous dispersion coefficients...

solute transport | discontinuous dispersion tensor | advection‐dispersion equation | reflection barrier | random walk particle tracking | DIFFUSION-PROCESSES | FIELD | IMPLEMENTATION | EQUATIONS | TRANSITION-PROBABILITY DENSITIES | WATER RESOURCES | SIMULATION | SOLUTE TRANSPORT | FLOW | ENVIRONMENTAL SCIENCES | SOIL | POROUS-MEDIA | LIMNOLOGY | Hydrology | Algorithms | High performance computing | Groundwater

solute transport | discontinuous dispersion tensor | advection‐dispersion equation | reflection barrier | random walk particle tracking | DIFFUSION-PROCESSES | FIELD | IMPLEMENTATION | EQUATIONS | TRANSITION-PROBABILITY DENSITIES | WATER RESOURCES | SIMULATION | SOLUTE TRANSPORT | FLOW | ENVIRONMENTAL SCIENCES | SOIL | POROUS-MEDIA | LIMNOLOGY | Hydrology | Algorithms | High performance computing | Groundwater

Journal Article

7.
Effect of Grain Boundary Segregation of Interstitial Elements on Hall-Petch Coefficient in Steels

MATERIALS TRANSACTIONS, ISSN 1345-9678, 01/2014, Volume 55, Issue 1, pp. 28 - 34

.... The Hall-Petch coefficient is as small as 150 MPa.mu m(1/2) in interstitial-free steels but it increases to 600 MPa.mu m(1/2...

interstitial free steel | FERRITIC STEEL | PHOSPHORUS | CARBON | grain boundary segregation | MATERIALS SCIENCE, MULTIDISCIPLINARY | METALLURGY & METALLURGICAL ENGINEERING | Hall-Petch coefficient | IRON | grain refinement strengthening | interstitial elements | YIELD-STRESS | AUSTENITIC STAINLESS-STEEL | DISLOCATION | dislocation pile-up | discontinuous yielding | POINT

interstitial free steel | FERRITIC STEEL | PHOSPHORUS | CARBON | grain boundary segregation | MATERIALS SCIENCE, MULTIDISCIPLINARY | METALLURGY & METALLURGICAL ENGINEERING | Hall-Petch coefficient | IRON | grain refinement strengthening | interstitial elements | YIELD-STRESS | AUSTENITIC STAINLESS-STEEL | DISLOCATION | dislocation pile-up | discontinuous yielding | POINT

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 01/2016, Volume 270, Issue 1, pp. 88 - 133

We consider the Lp solvability for divergence and non-divergence form Schrödinger equations with discontinuous coefficients...

Discontinuous coefficient | Schrödinger equation | MATHEMATICS | Schrodinger equation | SPACES | L(P) | DIRICHLET PROBLEM | VMO | ELLIPTIC-EQUATIONS | OPERATORS

Discontinuous coefficient | Schrödinger equation | MATHEMATICS | Schrodinger equation | SPACES | L(P) | DIRICHLET PROBLEM | VMO | ELLIPTIC-EQUATIONS | OPERATORS

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 06/2015, Volume 290, pp. 45 - 56

.... Galerkin formulation, which was proved to be coercive and well-posed for fractional diffusion equations with a constant diffusivity coefficient, may lose its coercivity for variable-coefficient problems...

Petrov–Galerkin finite element method | Weak coercivity | Fractional diffusion equations | Discontinuous Petrov–Galerkin framework | Discontinuous Petrov-Galerkin framework | Petrov-Galerkin finite element method | DISPERSION | CALCULUS | ELASTICITY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | DIFFERENCE METHOD | LEVY MOTION | TURBULENCE | CIRCULANT PRECONDITIONER | Finite element method | Methods | Magnetic properties | Mathematical analysis | Coercive force | Constants | Mathematical models | Diffusion | Galerkin methods | Convergence

Petrov–Galerkin finite element method | Weak coercivity | Fractional diffusion equations | Discontinuous Petrov–Galerkin framework | Discontinuous Petrov-Galerkin framework | Petrov-Galerkin finite element method | DISPERSION | CALCULUS | ELASTICITY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | DIFFERENCE METHOD | LEVY MOTION | TURBULENCE | CIRCULANT PRECONDITIONER | Finite element method | Methods | Magnetic properties | Mathematical analysis | Coercive force | Constants | Mathematical models | Diffusion | Galerkin methods | Convergence

Journal Article

Macromolecules, ISSN 0024-9297, 01/2016, Volume 49, Issue 2, pp. 634 - 642

The friction coefficient between Tetronic gel and water is measured as a function of the polymer concentration of the gel and the temperature by a simply designed apparatus...

DISCONTINUOUS VOLUME TRANSITIONS | NERVE | POLYMER SCIENCE | GELS | 3-DIMENSIONAL POLYMERS | BEHAVIOR | LIGHT-SCATTERING | MOLECULAR-SIZE DISTRIBUTION

DISCONTINUOUS VOLUME TRANSITIONS | NERVE | POLYMER SCIENCE | GELS | 3-DIMENSIONAL POLYMERS | BEHAVIOR | LIGHT-SCATTERING | MOLECULAR-SIZE DISTRIBUTION

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 06/2017, Volume 125, pp. 55 - 63

... and diffusion coefficients are possibly discontinuous.

Euler–Maruyama approximation | Discontinuous coefficients | Strong rate of convergence | Stochastic differential equation | Euler-Maruyama approximation | SDES | STATISTICS & PROBABILITY | Differential equations

Euler–Maruyama approximation | Discontinuous coefficients | Strong rate of convergence | Stochastic differential equation | Euler-Maruyama approximation | SDES | STATISTICS & PROBABILITY | Differential equations

Journal Article

Numerische Mathematik, ISSN 0029-599X, 05/2016, Volume 133, Issue 1, pp. 141 - 176

We propose and analyse a fully discrete discontinuous Galerkin time-stepping method for parabolic Hamilton-Jacobi-Bellman equations with Cordes coefficients...

65N15 | 65N12 | 35D35 | 35K55 | 65N30 | 35K10 | NUMERICAL-METHODS | MATHEMATICS, APPLIED | HP-VERSION | APPROXIMATION | DIFFERENCE-SCHEMES | Finite element method | Anisotropy | Methods | Mathematics - Numerical Analysis | Numerical Analysis | Mathematics

65N15 | 65N12 | 35D35 | 35K55 | 65N30 | 35K10 | NUMERICAL-METHODS | MATHEMATICS, APPLIED | HP-VERSION | APPROXIMATION | DIFFERENCE-SCHEMES | Finite element method | Anisotropy | Methods | Mathematics - Numerical Analysis | Numerical Analysis | Mathematics

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 7/2015, Volume 217, Issue 1, pp. 113 - 154

In this paper we study weakly hyperbolic second order equations with time dependent irregular coefficients...

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | MATHEMATICS, APPLIED | DISCONTINUOUS COEFFICIENTS | MECHANICS | REGULARITY | CAUCHY-PROBLEM | SYSTEMS | WELL-POSEDNESS | OPERATORS | Concretes | Construction | Archives | Mathematical analysis | Roots | Cauchy problem | Mathematics - Analysis of PDEs

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | MATHEMATICS, APPLIED | DISCONTINUOUS COEFFICIENTS | MECHANICS | REGULARITY | CAUCHY-PROBLEM | SYSTEMS | WELL-POSEDNESS | OPERATORS | Concretes | Construction | Archives | Mathematical analysis | Roots | Cauchy problem | Mathematics - Analysis of PDEs

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 6/2019, Volume 79, Issue 3, pp. 1572 - 1607

.... For linear problems with constant coefficients, it is well-known in the literature that the choice of the numerical flux (e.g. central or upwind...

Discontinuous Galerkin | 65N15 | Computational Mathematics and Numerical Analysis | 65N12 | Error analysis | 65N35 | Theoretical, Mathematical and Computational Physics | Summation-by-parts | 65N06 | Error bound | Mathematics | Algorithms | Flux reconstruction | Mathematical and Computational Engineering | Error growth | 65N30 | BY-PARTS OPERATORS | MATHEMATICS, APPLIED | SPLIT-FORM | CONSERVATION | Analysis | Environmental law | Methods | Differential equations | Mathematics - Numerical Analysis

Discontinuous Galerkin | 65N15 | Computational Mathematics and Numerical Analysis | 65N12 | Error analysis | 65N35 | Theoretical, Mathematical and Computational Physics | Summation-by-parts | 65N06 | Error bound | Mathematics | Algorithms | Flux reconstruction | Mathematical and Computational Engineering | Error growth | 65N30 | BY-PARTS OPERATORS | MATHEMATICS, APPLIED | SPLIT-FORM | CONSERVATION | Analysis | Environmental law | Methods | Differential equations | Mathematics - Numerical Analysis

Journal Article

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, ISSN 0764-583X, 02/2019, Volume 52, Issue 6, pp. 2457 - 2477

.... We show here how one can optimize transmission conditions to take benefit from the jumps in the coefficients of the problem, when they are aligned with the subdomain interface, and obtain methods which converge for two subdomains in certain situations independently of the mesh size, which would not be possible without jumps in the coefficients.

MATHEMATICS, APPLIED | Maxwell's equations | discontinuous coefficients | Domain decomposition | optimized Schwarz methods | Domain decomposition methods | Thermodynamics | Iterative methods | Coefficients | Mathematical analysis | Asymptotic methods

MATHEMATICS, APPLIED | Maxwell's equations | discontinuous coefficients | Domain decomposition | optimized Schwarz methods | Domain decomposition methods | Thermodynamics | Iterative methods | Coefficients | Mathematical analysis | Asymptotic methods

Journal Article

Journal of scientific computing, ISSN 1573-7691, 2016, Volume 70, Issue 2, pp. 662 - 685

... for the time discretization, where the diffusion coefficient depends on the unknown solution and is discontinuous across the interface...

Discontinuous Galerkin | Computational Mathematics and Numerical Analysis | Nonlinear | Parabolic | BDF | Theoretical, Mathematical and Computational Physics | Anti-symmetric | Mathematics | Algorithms | Appl.Mathematics/Computational Methods of Engineering | Interior penalty | Interface | Finite element | CONVECTION-DIFFUSION PROBLEMS | MATHEMATICS, APPLIED | APPROXIMATION | GALERKIN METHOD | FINITE-ELEMENT METHODS | FEM | ELLIPTIC INTERFACE PROBLEMS

Discontinuous Galerkin | Computational Mathematics and Numerical Analysis | Nonlinear | Parabolic | BDF | Theoretical, Mathematical and Computational Physics | Anti-symmetric | Mathematics | Algorithms | Appl.Mathematics/Computational Methods of Engineering | Interior penalty | Interface | Finite element | CONVECTION-DIFFUSION PROBLEMS | MATHEMATICS, APPLIED | APPROXIMATION | GALERKIN METHOD | FINITE-ELEMENT METHODS | FEM | ELLIPTIC INTERFACE PROBLEMS

Journal Article

Journal of computational physics, ISSN 0021-9991, 2017, Volume 335, pp. 497 - 515

We present a fast and accurate algorithm to solve Poisson problems in complex geometries, using regular Cartesian grids. We consider a variety of...

Embedded mesh | Poisson equation | Interface jump | High oder | Immersed method | Correction Function Method | BIHARMONIC-EQUATIONS | INTEGRAL-EQUATIONS | POTENTIAL-THEORY | PHYSICS, MATHEMATICAL | GHOST FLUID METHOD | DISCONTINUOUS COEFFICIENTS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | CONDITION CAPTURING METHOD | IRREGULAR DOMAINS | IMMERSED BOUNDARY METHOD | FINITE-ELEMENT-METHOD | Algorithms

Embedded mesh | Poisson equation | Interface jump | High oder | Immersed method | Correction Function Method | BIHARMONIC-EQUATIONS | INTEGRAL-EQUATIONS | POTENTIAL-THEORY | PHYSICS, MATHEMATICAL | GHOST FLUID METHOD | DISCONTINUOUS COEFFICIENTS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | CONDITION CAPTURING METHOD | IRREGULAR DOMAINS | IMMERSED BOUNDARY METHOD | FINITE-ELEMENT-METHOD | Algorithms

Journal Article

Numerische Mathematik, ISSN 0029-599X, 1/2018, Volume 138, Issue 1, pp. 219 - 239

...–Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient...

Secondary 65L20 | Stochastic differential equations | Discontinuous drift | Theoretical, Mathematical and Computational Physics | Mathematics | 65C20 | Euler–Maruyama method | Mathematical Methods in Physics | 65C30 | Strong convergence rate | Numerical Analysis | Mathematical and Computational Engineering | Mathematics, general | Degenerate diffusion | Numerical and Computational Physics, Simulation | Primary 60H10 | Euler-Maruyama method | MATHEMATICS, APPLIED | STOCHASTIC DIFFERENTIAL-EQUATIONS | NUMERICAL-METHOD | APPROXIMATIONS | REGULARITY | EXACT SIMULATION

Secondary 65L20 | Stochastic differential equations | Discontinuous drift | Theoretical, Mathematical and Computational Physics | Mathematics | 65C20 | Euler–Maruyama method | Mathematical Methods in Physics | 65C30 | Strong convergence rate | Numerical Analysis | Mathematical and Computational Engineering | Mathematics, general | Degenerate diffusion | Numerical and Computational Physics, Simulation | Primary 60H10 | Euler-Maruyama method | MATHEMATICS, APPLIED | STOCHASTIC DIFFERENTIAL-EQUATIONS | NUMERICAL-METHOD | APPROXIMATIONS | REGULARITY | EXACT SIMULATION

Journal Article