Pointwise A Posteriori Error Analysis of a Discontinuous Galerkin Method for the Elliptic Obstacle Problem

08/26/2021
βˆ™
by   Blanca Ayuso de Dios, et al.
βˆ™
0
βˆ™

We present a posteriori error analysis in the supremum norm for the symmetric interior penalty discontinuous Galerkin method for the elliptic obstacle problem. We construct discrete barrier functions based on appropriate corrections of the conforming part of the solution that is obtained via a constrained averaging operator. The corrector function accounts properly for the non-conformity of the approximation and it is estimated by direct use of the Green's function of the unconstrained elliptic problem. The use of the continuous maximum principle guarantees the validity of the analysis without mesh restrictions but shape regularity. The proposed residual type estimators are shown to be reliable and efficient. Numerical results in two dimensions are included to verify the theory and validate the performance of the error estimator.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 32

page 33

βˆ™ 09/29/2020

Residual-based a posteriori error estimates for 𝐑𝐩-discontinuous Galerkin discretisations of the biharmonic problem

We introduce a residual-based a posteriori error estimator for a novel h...
βˆ™ 04/16/2021

Unified Analysis of Discontinuous Galerkin Methods for Frictional Contact Problem with normal compliance

In this article, a reliable and efficient a posteriori error estimator o...
βˆ™ 08/09/2019

A posteriori error estimates for the mortar staggered DG method

Two residual-type error estimators for the mortar staggered discontinuou...
βˆ™ 12/07/2020

Multipatch Discontinuous Galerkin IGA for the Biharmonic Problem On Surfaces

We present the analysis of interior penalty discontinuous Galerkin Isoge...
βˆ™ 11/27/2019

A priori and a posteriori error analysis of an unfitted HDG method for semi-linear elliptic problems

We present a priori and a posteriori error analysis of a high order hybr...
βˆ™ 01/29/2021

Homogeneous multigrid for embedded discontinuous Galerkin methods

We introduce a homogeneous multigrid method in the sense that it uses th...
βˆ™ 07/11/2017

Functional approach to the error control in adaptive IgA schemes for elliptic boundary value problems

This work presents a numerical study of functional type a posteriori err...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.