A study of a modified scheme of the finite element method in the model problem of a crack (Q1096471)

The accuracy is studied of two modifications of the method of finite elements on six-point triangles as applied to the mixed problem for Laplace equation in a half-plane. An asymptotic expansion of the mesh solution is constructed showing that the coefficient at the principal term of the asymptotic expansion of the error is reduced by a factor of 8.5 and 16.5 for the two modifications studied, respectively, as compared with the unmodified case, even though the accuracy of the method remains at the level of O(h/\(\sqrt{r})\).