eprintid: 1572511
rev_number: 24
eprint_status: archive
userid: 608
dir: disk0/01/57/25/11
datestamp: 2018-03-02 12:50:18
lastmod: 2021-09-19 23:55:40
status_changed: 2018-03-02 12:50:18
type: article
metadata_visibility: show
creators_name: Smears, I
creators_name: Sueli, E
title: Discontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations With Cordes Coefficients
ispublished: pub
divisions: UCL
divisions: B04
divisions: C06
divisions: F59
keywords: Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, discontinuous Galerkin, hp-DGFEM, Cordes condition, nondivergence form, discontinuous coefficients, PDEs, finite element methods, CONVERGENCE, VERSION
note: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
abstract: Nondivergence form elliptic equations with discontinuous coefficients do not generally possess a weak formulation, thus presenting an obstacle to their numerical solution by classical finite element methods. We propose a new $hp$-version discontinuous Galerkin finite element method for a class of these problems which satisfy the Cordès condition. It is shown that the method exhibits a convergence rate that is optimal with respect to the mesh size $h$ and suboptimal with respect to the polynomial degree $p$ by only half an order. Numerical experiments demonstrate the accuracy of the method and illustrate the potential of exponential convergence under $hp$-refinement for problems with discontinuous coefficients and nonsmooth solutions.
date: 2013-01-01
date_type: published
publisher: SIAM PUBLICATIONS
official_url: http://dx.doi.org/10.1137/120899613
oa_status: green
full_text_type: pub
language: eng
primo: open
primo_central: open_green
article_type_text: Article
verified: verified_manual
elements_id: 1419012
doi: 10.1137/120899613
lyricists_name: Smears, Iain
lyricists_id: ISMEA05
actors_name: Smears, Iain
actors_id: ISMEA05
actors_role: owner
full_text_status: public
publication: SIAM: Journal on Numerical Analysis
volume: 51
number: 4
pagerange: 2088-2106
pages: 19
issn: 1095-7170
citation:        Smears, I;    Sueli, E;      (2013)    Discontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations With Cordes Coefficients.                   SIAM: Journal on Numerical Analysis , 51  (4)   pp. 2088-2106.    10.1137/120899613 <https://doi.org/10.1137/120899613>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1572511/1/SIAM%20J.%20Numer.%20Anal.%202013%20Smears.pdf