H-adaptive Element-Free Trefftz Method

Abstract

The Element-Free Trefftz method can solve the problem only by taking the collocation points on the boundary when the domain under consideration is governed by the linear and homogeneous differentia equation. Only the coordinates and the boundary-specified values on the boundary collocation points are required as the input data and therefore, input data generation is much simpler than the other solution procedures. However, the computational accuracy is strongly dependent on the positions of the collocation points. For determining the positions with the desired accuracy, this paper presents h-daptive scheme for the placement of the collocation points. Global and local error estimators are defined by the residuals of the boundary conditions. The refinement of the positions is performed so that new collocation points are placed in the center of the boundary segments with larger local error estimators than the global estimator. The present scheme is applied to the two-dimensional potential problem in order to confirm its validity.