A high order discontinuous Galerkin Nitsche method for elliptic problems with fictitious boundary
type: Item
instance of: scholarly article
title: A high order discontinuous Galerkin Nitsche method for elliptic problems with fictitious boundary
zbMATH Open document ID: 1269.65126
author: A. Johansson
author: Mats G. Larson
published in: Numerische Mathematik
publication date: 2013-04-03T00:00:00Z
review text: In order to solve elliptic problems on domains with an immersed boundary representation on a structured grid, the authors use Nitche's method (concerning weak enforcement of Dirichlet boundary conditions) to formulate a discontinuous Galerkin method. The method avoids using very small elements on the boundary by associating them to a neighboring element with a sufficiently large intersection with the domain. Optimal order a priori error estimates are derived and illustrated by numerical examples for linear and quadratic bases. The numerical stability of the method is investigated by theoretical bounds on the condition number of the stiffness matrix. Numerical examples illustrate the implementation of the method.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 6150055
zbMATH Keywords: discontinuous Galerkin Nitsche method
zbMATH Keywords: error estimates
zbMATH Keywords: condition number
zbMATH Keywords: numerical examples
zbMATH Keywords: stability
reviewed by: Adrian Carabineanu
MaRDI profile type: Publication
full work available at URL: s00211-012-0497-1
OpenAlex ID: W2026370306
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DOI: 10.1007/S00211-012-0497-1
description: scientific article; zbMATH DE number 6150055