A Priori Anisotropic Mesh Adaptation on Implicitly Defined Surfaces

Mesh adaptation on surfaces demands particular care due to the important role played by the surface fitting. We propose an adaptive procedure based on a new error analysis which combines a rigorous anisotropic estimator for the $L^1$-norm of the interpolation error with an anisotropic heuristic control of the geometric error. We resort to a metric-based adaptive algorithm which employs local operations to modify the initial mesh according to the information provided by the error analysis. An extensive numerical validation corroborates the robustness of the error analysis as well as of the adaptive procedure