Numerical analysis of a class of penalty discontinuous Galerkin methods for nonlocal diffusion problems
DOI10.1051/m2an/2024064MaRDI QIDQ6652084
Jianfang Lu, Lili Ju, Qiang Du, Xiaochuan Tian
Publication date: 12 December 2024
Published in: European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)
Numerical methods for integral equations (65R20) Diffusion (76R50) Heat equation (35K05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) 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) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Linear integral equations (45A05)
Cites Work
- Unnamed Item
- Continuous and discontinuous finite element methods for a peridynamics model of mechanics
- Numerical solutions of partial differential equations
- Efficient implementation of essentially nonoscillatory shock-capturing schemes
- TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
- The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
- A discontinuous \(hp\) finite element method for convection-diffusion problems
- Nonlocal convection-diffusion problems and finite element approximations
- A weak Galerkin finite element method for second-order elliptic problems
- Reformulation of elasticity theory for discontinuities and long-range forces
- Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I
- Nonlocal trace spaces and extension results for nonlocal calculus
- Mathematics of smoothed particle hydrodynamics: a study via nonlocal Stokes equations
- A discontinuous Galerkin method with penalty for one-dimensional nonlocal diffusion problems
- Regularity analyses and approximation of nonlocal variational equality and inequality problems
- Nodal discontinuous Galerkin methods for fractional diffusion equations on 2D domain with triangular meshes
- Sparse grid discontinuous Galerkin methods for high-dimensional elliptic equations
- Nonlocal convection-diffusion volume-constrained problems and jump processes
- Mathematical analysis for the peridynamic nonlocal continuum theory
- Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models
- Nonconforming Discontinuous Galerkin Methods for Nonlocal Variational Problems
- A Nonlocal Vector Calculus with Application to Nonlocal Boundary Value Problems
- Nonlocal Operators with Applications to Image Processing
- The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
- The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
- Nonlocal Linear Image Regularization and Supervised Segmentation
- Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
- An Analysis of the Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems
- Total-Variation-Diminishing Time Discretizations
- TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
- The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- A Quasi-nonlocal Coupling Method for Nonlocal and Local Diffusion Models
- Nonlocal Conservation Laws. A New Class of Monotonicity-Preserving Models
- Nonlocal Modeling, Analysis, and Computation
- Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
- A discontinuous Galerkin method for one-dimensional time-dependent nonlocal diffusion problems
- Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
- A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
- Stability of a Nonlocal Traffic Flow Model for Connected Vehicles
- Nonlocal Wave Propagation in Unbounded Multi-Scale Media
- Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models
- Stability and accuracy of time‐stepping schemes and dispersion relations for a nonlocal wave equation
- The Direct Discontinuous Galerkin (DDG) Methods for Diffusion Problems
- Local Discontinuous Galerkin methods for fractional diffusion equations
- Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations
- The bond-based peridynamic system with Dirichlet-type volume constraint
- Discontinuous Galerkin Method for Fractional Convection-Diffusion Equations
- The Mathematical Theory of Finite Element Methods
- A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives
- Nonconforming Elements in the Finite Element Method with Penalty
- Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization
- Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen--Cahn Equations
- Numerical methods for nonlocal and fractional models
- Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations
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