Optimal stabilization and time step constraints for the forward Euler-local discontinuous Galerkin method applied to fractional diffusion equations
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Publication:2222302
DOI10.1016/j.jcp.2019.06.005zbMath1452.65228OpenAlexW2951173097WikidataQ127728833 ScholiaQ127728833MaRDI QIDQ2222302
Publication date: 26 January 2021
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2019.06.005
Courant-Friedrichs-Lewy conditionlocal discontinuous Galerkin methodvon Neumann stability analysisRiesz and Riemann Liouville operators
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11)
Related Items (4)
Local discontinuous Galerkin method for the fractional diffusion equation with integral fractional Laplacian ⋮ On the convergence of the local discontinuous Galerkin method applied to a stationary one dimensional fractional diffusion problem ⋮ Non-uniform L1/discontinuous Galerkin approximation for the time-fractional convection equation with weak regular solution ⋮ Study of the backward difference and local discontinuous Galerkin (LDG) methods for solving fourth-order partial integro-differential equations (PIDEs) with memory terms: stability analysis
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
- Finite element approximation of fractional order elliptic boundary value problems
- CFL conditions for Runge-Kutta discontinuous Galerkin methods on triangular grids
- Optimal error estimates for the fully discrete interior penalty DG method for the wave equation
- Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients
- Compact finite difference method for the fractional diffusion equation
- Semi discrete discontinuous Galerkin methods and stage-exceeding-order, strong-stability-preserving Runge-Kutta time discretizations
- Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids
- Efficient implementation of essentially nonoscillatory shock-capturing schemes
- Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
- An \(hp\)-analysis of the local discontinuous Galerkin method for diffusion problems
- On the conservation of fractional nonlinear Schrödinger equation's invariants by the local discontinuous Galerkin method
- A unified Petrov-Galerkin spectral method for fractional PDEs
- A review of applications of fractional calculus in Earth system dynamics
- Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains
- A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
- A fast finite difference method for three-dimensional time-dependent space-fractional diffusion equations with fractional derivative boundary conditions
- Analysis of local discontinuous Galerkin method for time-space fractional convection-diffusion equations
- A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations
- The role of fractional calculus in modeling biological phenomena: a review
- A novel finite volume method for the Riesz space distributed-order advection-diffusion equation
- Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver
- A PDE approach to fractional diffusion in general domains: a priori error analysis
- Nodal discontinuous Galerkin methods for fractional diffusion equations on 2D domain with triangular meshes
- A general finite element formulation for fractional variational problems
- An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems
- A hybridized discontinuous Galerkin method for 2D fractional convection-diffusion equations
- A second-order accurate numerical approximation for the fractional diffusion equation
- Finite difference methods for two-dimensional fractional dispersion equation
- An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
- Optimal a priori error estimates for the $hp$-version of the local discontinuous Galerkin method for convection--diffusion problems
- Fronts in anomalous diffusion–reaction systems
- A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
- Taming the CFL Number for Discontinuous Galerkin Methods on Structured Meshes
- The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
- Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains
- A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
- A Fast Finite Difference Method for Two-Dimensional Space-Fractional Diffusion Equations
- High-Order Accurate Runge-Kutta (Local) Discontinuous Galerkin Methods for One- and Two-Dimensional Fractional Diffusion Equations
- Error Analysis of a Finite Element Method for the Space-Fractional Parabolic Equation
- High‐order algorithms for Riesz derivative and their applications (V)
- Local Discontinuous Galerkin methods for fractional diffusion equations
- Discontinuous Galerkin Method for Fractional Convection-Diffusion Equations
- Variational formulation for the stationary fractional advection dispersion equation
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