A node reconnection algorithm for mimetic finite difference discretizations of elliptic equations on triangular meshes

Abstract

Most efficient adaptive mesh methods employ a few strategies, including local mesh refinement (h-adaptation), movement of mesh nodes (r-adaptation), and node reconnection (c-adaptation). Despite its simplicity, node reconnection methods are seldom analyzed apart from the other adaptation methods even in applications where severe restrictions are imposed on topological operations with a mesh. However, using only node reconnection the discretization error can be significantly reduced. In this paper, we develop and numerically analyze a new c-adaptation algorithm for mimetic finite difference discretizations of elliptic equations on triangular meshes. Our algorithm is based on a new error indicator for such discretizations, which can also be used for unstructured general polygonal meshes. We demonstrate the efficiency of our new algorithm with numerical examples.