A numerical method for fractal conservation laws
From MaRDI portal
Publication:3584769
DOI10.1090/S0025-5718-09-02293-5zbMath1201.65163MaRDI QIDQ3584769
Publication date: 30 August 2010
Published in: Mathematics of Computation (Search for Journal in Brave)
convergencenumerical resultsintegral operatorfractal operatorLevy operatorfractal scalar conservation law
Integro-partial differential equations (45K05) Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Initial value problems for PDEs with pseudodifferential operators (35S10)
Related Items
A Monotone Discretization for Integral Fractional Laplacian on Bounded Lipschitz Domains: Pointwise Error Estimates under Hölder Regularity ⋮ Robust Numerical Methods for Nonlocal (and Local) Equations of Porous Medium Type. Part II: Schemes and Experiments ⋮ Finite element method for a space-fractional anti-diffusive equation ⋮ Explicit representations for multiscale Lévy processes and asymptotics of multifractal conservation laws ⋮ A direct discontinuous Galerkin method for a high order nonlocal conservation law ⋮ Numerical approximations for fractional elliptic equationsviathe method of semigroups ⋮ Uniform tail estimates and \(L^p( {\mathbb{R}}^N) \)-convergence for finite-difference approximations of nonlinear diffusion equations ⋮ Finite difference methods for the generator of 1D asymmetric alpha-stable Lévy motions ⋮ Simultaneous denoising and enhancement of signals by a fractal conservation law ⋮ The discontinuous Galerkin method for fractional degenerate convection-diffusion equations ⋮ Multilevel Monte Carlo Finite Difference Methods for Fractional Conservation Laws with Random Data ⋮ Linearized difference schemes for a BBM equation with a fractional nonlocal viscous term ⋮ Numerical approximation of the integral fractional Laplacian ⋮ LDG approximation of a nonlinear fractional convection-diffusion equation using B-spline basis functions ⋮ Mathematical and numerical analysis of initial boundary value problem for a linear nonlocal equation ⋮ Entropy solution theory for fractional degenerate convection-diffusion equations ⋮ Efficient numerical schemes for fractional water wave models ⋮ Convergence of a stochastic particle approximation for fractional scalar conservation laws ⋮ The local discontinuous Galerkin method for convection-diffusion-fractional anti-diffusion equations ⋮ Solving a non-linear fractional convection-diffusion equation using local discontinuous Galerkin method ⋮ On numerical methods and error estimates for degenerate fractional convection-diffusion equations ⋮ Multiscale conservation laws driven by Lévy stable and Linnik diffusions: asymptotics, shock creation, preservation and dissolution ⋮ Robust Numerical Methods for Nonlocal (and Local) Equations of Porous Medium Type. Part I: Theory ⋮ On the spectral vanishing viscosity method for periodic fractional conservation laws ⋮ Numerical investigation of the variable-order fractional Sobolev equation with non-singular Mittag-Leffler kernel by finite difference and local discontinuous Galerkin methods
Cites Work
- Numerical study of interacting particles approximation for integro-differential equations
- A non-monotone nonlocal conservation law for dune morphodynamics
- Entropy formulation for fractal conservation laws
- Compact sets in the space \(L^ p(0,T;B)\)
- Fractal Burgers equations
- Global solution and smoothing effect for a non-local regularization of a hyperbolic equation.
- Numerical approximation of hyperbolic systems of conservation laws
- Probabilistic approximation and inviscid limits for one-dimensional fractional conservation laws
- Dislocation dynamics: Short-time existence and uniqueness of the solution
- Fractal first-order partial differential equations
- Semi-groupes de Feller sur une variété à bord compacte et problèmes aux limites intégro-différentiels du second ordre donnant lieu au principe du maximum
- Asymptotics for conservation laws involving Lévy diffusion generators
- OCCURRENCE AND NON-APPEARANCE OF SHOCKS IN FRACTAL BURGERS EQUATIONS
- Convergence Analysis of a Mixed Finite Volume Scheme for an Elliptic-Parabolic System Modeling Miscible Fluid Flows in Porous Media
- Well-posedness and numerical analysis of a one-dimensional non-local transport equation modelling dislocations dynamics
- Analysis of a circulant based preconditioner for a class of lower rank extracted systems
- Optimal Control with State-Space Constraint. II
- Instabilities and Nonlinear Patterns of Overdriven Detonations in Gases
- Conjugate Gradient Methods for Toeplitz Systems
- Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item