An Edge-Based Anisotropic Mesh Refinement Algorithm and Its Application to Interface Problems (Communications in Computational Physics, 2010)
Based on an error estimate in terms of element edge vectors on arbitraryunstructured simplex meshes, we propose a new edge-based anisotropic mesh refinementalgorithm. As the mesh adaptation indicator, the error estimate involves only thegradient of error rather than higher order derivatives. The preferred refinement edgeis chosen to reduce the maximal term in the error estimate. The algorithm is implementedin both two- and three-dimensional cases, and applied to the singular functioninterpolation and the elliptic interface problem. The numerical results demonstratethat the convergence order obtained by using the proposed anisotropic mesh refinementalgorithm can be higher than that given by the isotropic one.