A Directional Error Estimator for Adaptive Finite Element Analysis

Abstract. We present an error estimator based on firstand second-order derivatives recovery for finite element adaptive analysis. At first, we briefly discuss the abstract framework of the adopted error estimation techniques. Some possibilities of derivatives recovery are considered, including the proposal of a directional error estimator. Using the directional error estimator proposed, an adaptive finite element analysis is performed which gives an adapted mesh where the estimated error is uniformly distributed over the domain. The advantages of adapting meshes are well known, but we place particular emphasis on the anisotropic mesh adaptation process generated by the directional error estimator. This mesh adaptation process gives improved results in localizing regions of rapid or abrupt variations of the variables, whose location is not known a priori. We apply the above abstract formulation to analyze the behaviour of the recovery technique and the proposed adaptive process for some particular functions. Finally, we apply the procedure to some finite element models for limit analysis.