Adaptive Edge Element Approximation for H(curl) Elliptic Variational Inequalities of Second Kind
Publication in refereed journal

香港中文大學研究人員
替代計量分析
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其它資訊
摘要This paper is concerned with the analysis of an adaptive edge element method for solving elliptic $curl$-$curl$ variational inequalities of second kind. We derive a posteriori error estimators based on a special combination of the Moreau--Yosida regularization and Nédélec's edge elements of first family. With the help of these a posteriori error estimators, an AFEM algorithm is proposed and studied. We are able to establish both the reliability and the efficiency of these estimators, by means of a special linear auxiliary problem involving the discrete Moreau--Yosida-regularized dual formulation, along with a local regular decomposition for $H(curl)$-functions and the bubble functions. Furthermore, we demonstrate the strong convergence of the sequence of the edge element solutions generated by the adaptive algorithm toward the solution of a limiting problem, by first achieving the convergence of the maximal error indicator and the residual corresponding to the sequence of the adaptive edge element solutions, under a reasonable condition on the regularization parameter in terms of the adaptive mesh size. Three-dimensional numerical experiments are presented to verify the robustness and effectiveness of the adaptive algorithm when it is applied to a problem arising from the type-II (high-temperature) superconductivity.
出版社接受日期08.04.2020
著者Malte Winckler, Irwin Yousept, Jun Zou
期刊名稱SIAM Journal on Numerical Analysis
出版年份2020
月份6
卷號58
期次3
出版社Society for Industrial and Applied Mathematics
頁次1941 - 1964
國際標準期刊號0036-1429
電子國際標準期刊號1095-7170
語言美式英語
關鍵詞curl-curl elliptic variational inequalities, a posteriori error analysis, Moreau--Yosida regularization, edge elements, convergence analysis, superconductivity

上次更新時間 2020-18-09 於 00:16