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.
"A node reconnection algorithm for mimetic finite difference discretizations of elliptic equations on triangular meshes." Commun. Math. Sci. 3 (4) 665 - 680, December 2005.