An Adaptive FEM for a Maxwell Interface Problem

• DOI: 10.1007/s10915-015-0098-0
• Publication Date: 2015-09-12T12:00:48Z
• Authors: Huoyuan Duan; Fengjuan Qiu; Roger C. E. Tan; Weiying Zheng
• Keywords: Curl (programming language)

This paper develops an adaptive edge finite element method for a Maxwell interface problem: $$ {\mathbf{curl}}\mu ^{-1} {\mathbf{curl}}u_\delta +\delta \varepsilon u_\delta =f, $$curlμ-1curlu?+??u?=f, where $$\delta >0$$?>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.