New recovery error indicator for adaptive finite-element analysis on waveguiding structures

Abstract

The adaptive finite-element method (FEM) is an iterative variant of the FEM where, in a first step, an initial mesh with few and low-order elements is generated, the corresponding algebraic problem is solved and the error in the solution is estimated in order to add degrees of freedom in those regions of the domain with the biggest error estimation. This process is repeated until an ending condition is reached. The two basic stages in this method are the error indication and the mesh enrichment. In this paper, within the analysis of waveguiding structures, a new error indicator based on the curl recovery is described. In addition, an overview on refinement techniques is presented, and the -refinement employed in this study is briefly described. Results obtained with the curl-recovery indicator are discussed and compared with the classical nonadaptive FEM and two previously developed error indicators: the residual and flux continuity indicators.