Abstract
Nonconforming combinations are provided for solving interface problems of elliptic equations. In these approaches, the Ritz-Galerkin method with particular solutions is used for the part of a solution domain where there are interface singular points; and the conventional finite element method is used for the rest of the solution domain. In addition, admissible functions chosen are constrained to be continuous only at the element nodes on the common boundary of the subdomains. Error bounds are derived in the Sobolev norms, and numerical experiments are given for solving a model interface problem of the equation, − Δu + u = 0. Moreover, a significant coupling relation, L + 1 = O(|ln h|), is found for interface problems by using the nonconforming combinations, where ( L + 1) is the total number of particular solutions used in the Ritz-Galerkin method, and h is the maximal boundary length of triangular elements in the finite element method.
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