A-POSTERIORI ERROR INDICATOR AND ERROR ESTIMATORS FOR ADAPTIVE MESH REFINEMENT

Two different 'a posteriori' error estimation techniques are proposed in this paper. The effectiveness of the error estimates in adaptive me sh refinement for 2D and 3D electrostatic problems are also analyzed w ith numerical test results. The post-processing method employs an impr oved solution to estimate the error, whereas the gradient of field met hod utilizes the gradient of the field solution for estimating the 'a posterior' error. The gradient of field method is computationally inex pensive, since it solves a local problem on a patch of elements. The e rror estimates are tested by solving a set of self-adjoint boundary va lue problems in 2D and 3D using a hierarchical minimal tree based mesh refinement algorithm. The numerical test results and the performance evaluation establish the effectiveness of the proposed error estimates for adaptive mesh refinement.