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SUMMARYCombinations of the Ritz-Galerkin and finite element methods are applied to solving singularity problems of homogeneous, elliptic equations. The Ritz-Galerkin method is used in the subdomains where there exist singular points; and the finite element method is still used in the rest of the solution domains. More general coupling techniques than those of Reference 6 along the common boundary of subdomains are discussed.Numerical experiments using these kinds ofcoupling techniques are provided for the first time. It is interesting that the calculated results of Motz's problem have shown the simplified hybrid strategy in Reference 6 to be optimal for both error bounds and stability of numerical solutions, among all general coupling techniques.

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