Finite element method for solving problems with singular solutions

Numerical treatment of the elliptic boundary value problem with nonsmooth solution by the finite element method is discussed. The nonsmoothness could have its origin in the unsmooth boundary or the differential equation. This paper, which is a survey of the recent results, elaborates among others on the method of auxiliary mapping, the partition of unity finite element method and the hp version of FEM in three-dimensions. Numerical examples illustrate mathematical results.