An Improved Adaptive Mesh Refinement Method Based on Boundary Condition

For a posteriori error (PE) estimates obtained from single tetrahedron, the continuity between this tetrahedron and adjacent elements is ignored. This paper presents an adaptive mesh refinement method which improves the PE according to the boundary conditions. In this method, an error denoting the discontinuity of the finite element (FE) solution across the internal triangular faces is obtained and then, allocate the error on face to the original PE on both sides. At the same time, the scaling factor on vertices for mesh refinement is connected with the error on faces. Therefore, the PE will be more valid physically. Numerical results are presented and compared with original method to illustrate the performance of the proposed method.