An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms

Abstract

Abstract.Existence, uniqueness and error estimates for Ritz-Galerkin methods are o discussed in the case where the associated bilinear form satisfies a Carding type inequality, i.e., it is indefinite in a certain way. An application to the finite element method is given.In this note, we would like to discuss existence, uniqueness and estimates over the whole domain for some Ritz-Galerkin methods where the bilinear form satisfies o a Garding type inequality, i.e., it is indefinite in a special way. We shall first illustrate the problem by an example.For simplicity, let £2 be a simply connected convex region in the plane with a polygonal boundary d£2 and consider the Dirichlet problem

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