Some applications of the Trefftz method in linear elliptic boundary-value problems

Abstract

A generalized Trefftz method is developed for the boundary-value problems of a linear elliptic partial differential equation system in a more general sense. The approximate solution is constructed by a complete and regular set of Trefftz functions satisfying the differential equations within the domain. Unknown parameters are determined through minimizing the generalized complementary energy functional. Applications of the method to two-dimensional potential problems, plane elasticity and plate bending problems are discussed in detail. The numerical examples show that the presented method is efficient and accurate.