An a-posteriori error estimate for hp-adaptive DG methods for convection-diffusion problems on anisotropically refined meshes

Authors:
Stefano Giani;Dominik Schötzau;Liang Zhu
Affiliations:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK;Mathematics Department, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada;Mathematics Department, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada
Venue:
Computers & Mathematics with Applications
Year:
2014

Citing 10
Cited 1

The p and hp versions of the finite element method for problems with boundary layers

Mathematics of Computation
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling

SIAM Journal on Matrix Analysis and Applications
A Local Problem Error Estimator for Anisotropic Tetrahedral Finite Element Meshes

SIAM Journal on Numerical Analysis
A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems

SIAM Journal on Numerical Analysis
Robust A Posteriori Error Estimates for Stationary Convection-Diffusion Equations

SIAM Journal on Numerical Analysis
Hybrid scheduling for the parallel solution of linear systems

Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes

SIAM Journal on Scientific Computing
Discontinuous Galerkin methods on hp-anisotropic meshes I: a priori error analysis

International Journal of Computing Science and Mathematics
Discontinuous Galerkin methods on hp-anisotropic meshes II: a posteriori error analysis and adaptivity

Applied Numerical Mathematics
A robust a-posteriori error estimator for discontinuous Galerkin methods for convection--diffusion equations

Applied Numerical Mathematics

Editorial: High-order finite element approximation for partial differential equations

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.09

Visualization

Abstract

We prove an a-posteriori error estimate for hp-adaptive discontinuous Galerkin methods for the numerical solution of convection-diffusion equations on anisotropically refined rectangular elements. The estimate yields global upper and lower bounds of the errors measured in terms of a natural norm associated with diffusion and a semi-norm associated with convection. The anisotropy of the underlying meshes is incorporated in the upper bound through an alignment measure. We present a series of numerical experiments to test the feasibility of this approach within a fully automated hp-adaptive refinement algorithm.