Remeshing criteria and proper error representations for goal oriented h-adaptivity

Abstract

A key ingredient in h-adaptivity pertains to the transformation of output data from a given error estimator into input data, usually in the form of an element-size distribution, that needs to be supplied to a mesh generator.

This paper analyzes the different possibilities of defining remeshing criteria in the framework of goal oriented adaptivity. In standard energy norm driven adaptivity, the optimal mesh is clearly obtained if the local error distribution is uniform. The goal-oriented paradigm introduces new difficulties associated with the different possibilities for the spatial error representation and the signs of the local error contributions.

A nodal error representation is introduced in order to improve the communication with the automatic mesh generation tool, precluding the transfer of information from elements to nodes.

Numerical experiments demonstrate the ability of the introduced remeshing strategies to drive efficient adaptive procedures and to control the error in quantities of interest. The results of the numerical tests fit the expected properties of the different remeshing strategies.