On the Numerical Treatment of Boundary Singularities in Elliptic Problems
Abstract
Techniques are considered for improving the numerical approximation to a problem which possesses corner singularities. The particular problem considered here is taken from solid state electronics. Relined numerical solutions are obtained using two techniques. The first employs a nonuniform grid with a smaller spacing of the mesh points in the neighbourhood of the singularities. The second technique involves a transformation of the problem to one which is free from singularities. The dynamic ADI method, which needs no a priori relaxation parameters to accelerate convergence, is used to solve the discretized problem in both cases.
 Publication:

Journal of Computational Physics
 Pub Date:
 June 1986
 DOI:
 10.1016/00219991(86)900446
 Bibcode:
 1986JCoPh..64..459P