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Journal of Scientific Computing

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12-09-2015

An Adaptive FEM for a Maxwell Interface Problem

Authors: Huoyuan Duan, Fengjuan Qiu, Roger C. E. Tan, Weiying Zheng

Published in: Journal of Scientific Computing | Issue 2/2016

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Abstract

This paper develops an adaptive edge finite element method for a Maxwell interface problem: \( {\mathbf{curl}}\mu ^{-1} {\mathbf{curl}}u_\delta +\delta \varepsilon u_\delta =f, \) where \(\delta >0\) is allowed to degenerate to zero. A residual-based a posteriori error estimator is analyzed, with \(\delta \)-uniform lower and (global and local) upper error bounds. \(\delta \)-uniform convergence and optimality of the adaptive algorithm are also established. Numerical results are also presented.

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\(\hat{z}\) is obtained by multiplying the transposed Jacobian matrix of the affine mapping to the composition of z and the affine mapping (see (5.33) in [39, p. 129]).

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Title: An Adaptive FEM for a Maxwell Interface Problem
Authors: Huoyuan Duan
Fengjuan Qiu
Roger C. E. Tan
Weiying Zheng
Publication date: 12-09-2015
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 2/2016
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0098-0

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