Abstract
A noncomforming combined method of the Ritz-Galerkin and finite element methods is applied in solving unbounded domain problems of the equation, − Δu + u = 0. The Ritz-Galerkin method is used in an exterior subdomain; and the traditional finite element method is used in a bounded subdomain. Errors of numerical solutions have been derived in the Sobolev norms, and a significant coupling relation N + 1 = O(|ln h|) as h → 0 is found, where N + 1 is the total number of asymptotic particula Ritz-Galerkin method, and h is the maximal boundary length of triangular elements used in the finite element method. Numerical experiments have been carried out for a model problem on unbounded domains by using the nonconforming combination and the coupling strategy (1), showing that only two or three terms (i.e., N + 1 = 2 or 3) of particular solutions near the infinity are, in general cases, required for good approximate solutions in engineering application.
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