A local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations

DOI10.1016/j.jcp.2021.110894OpenAlexW4200517995MaRDI QIDQ2134809

Assyr Abdulle, Giacomo Rosilho de Souza

Publication date: 3 May 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.07148

zbMATH Keywords

elliptic equationa posteriori error estimatorsdiscontinuous Galerkinlocal scheme

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Elliptic equations and elliptic systems (35Jxx)

Uses Software

• libMesh

Cites Work

• Mathematical aspects of discontinuous Galerkin methods.
• An optimal Poincaré inequality for convex domains
• Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods
• Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems
• A posteriori error estimators for locally conservative methods of nonlinear elliptic problems
• Mixed finite elements in \(\mathbb{R}^3\)
• A unified approach to a posteriori error estimation using element residual methods
• An accurate \(\mathbf H\)(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems
• Guaranteed and robusta posteriorierror estimates for singularly perturbed reaction–diffusion problems
• Equilibrated error estimators for discontinuous Galerkin methods
• A discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally small and anisotropic diffusivity
• Some A Posteriori Error Estimators for Elliptic Partial Differential Equations
• The Fast Adaptive Composite Grid (FAC) Method for Elliptic Equations
• An Interior Penalty Finite Element Method with Discontinuous Elements
• Mixed and Hybrid Finite Element Methods
• Multi-Level Adaptive Solutions to Boundary-Value Problems
• A‐posteriori error estimates for the finite element method
• Error Estimates for Adaptive Finite Element Computations
• A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
• A Convergent Adaptive Algorithm for Poisson’s Equation
• A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations
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