Relevant, Purpose Based Error Criteria for Adaptive Finite Element Mesh Generation

Abstract

Several error criteria have made the scientific scene for purposes of adaptive finite element mesh generation. However, it is demonstrated in this paper, that when applied to the same problem, they give very different meshes as iterations on the mesh proceed. A comparison of the various criteria is made and it is shown that different measures of error give better values of different physical quantities, such as energy, flux density and potential. The choice of error criterion, therefore, rather than being arbitrary, should be based on the design task at hand.