SOME APPLICATIONS OF THE TREFFTZ METHOD IN LINEAR ELLIPTIC BOUNDARY-VALUE-PROBLEMS

A generalized Trefftz method is developed for the boundary-value probl ems of a linear elliptic partial differential equation system in a mor e general sense. The approximate solution is constructed by a complete and regular set of Trefftz functions satisfying the differential equa tions within the domain. Unknown parameters are determined through min imizing 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 exam ples show that the presented method is efficient and accurate.