An a posteriori error indicator for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

An a posteriori error indicator for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations

Authors:	Houston, Paul Perugia, Ilaria Schotzau, Dominik

Affiliation:	¹ School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK, ² Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy, ³ Mathematics Department, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada

Abstract:	^ Email: paul.houston{at}nottingham.ac.uk^* Corresponding author. Email: ilaria.perugia{at}unipv.it^**** Email: schoetzau{at}math.ubc.ca We introduce a residual-based a posteriori error indicator fordiscontinuous Galerkin discretizations of H(curl; ${Omega}$ )-ellipticboundary value problems that arise in eddy current models. Weshow that the indicator is both reliable and efficient withrespect to the approximation error measured in terms of a naturalenergy norm. We validate the performance of the indicator withinan adaptive mesh refinement procedure and show its asymptoticexactness for a range of test problems.

Keywords:	discontinuous Galerkin methods a posteriori error analysis eddy current problems
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