Comparison of two methods for the computation of singular solutions in elliptic problems
Specific properties of two methods for numerically solving elliptic problems with boundary singularities are compared by applying them both to the cracked beam problem. The methods have been analyzed in two previous papers in joint work by the first author. The first method is the integrated singular basis function method (ISBFM), while the second can be viewed as a variant of it. Both methods are finite element methods; with ISBFM, both the regular and singular part of the solution are approximated near the singularity, whereas with the second method, called singular function boundary integral method, only the singular part is approximated. The two methods prove to be accurate in estimating the leading singular coefficients; ISBFM is more stable and accurate, except for the second and third singular coefficients, because of the regular part approximation; on the other hand, the singular function boundary integral method is less costly to apply.
integrated singular basis function method
singular function boundary integral method
scientific article; zbMATH DE number 1022224