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


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.
著者Malte Winckler, Irwin Yousept, Jun Zou
期刊名稱SIAM Journal on Numerical Analysis
出版社Society for Industrial and Applied Mathematics
頁次1941 - 1964
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