Part II Nonconforming Combinations for Solving Elliptic Problems with Singularities

For solving elliptic problems with singularities, a nonconforming combined approach of the Ritz-Galerkin and finite element methods is presented. In this approach, singular functions are chosen to be admissible functions in the part of a solution domain where singularities exist; and piecewise linear (or bilinear) functions are chosen to be admissible functions in the rest of that solution domain. In addition, the admissible functions used here are constrained to be continuous only at the element modes on the common boundary of both methods. This method is nonconforming; however, the nonconforming effect does not result in larger errors of numerical solutions as long as a suitable coupling strategy is used…