General aspects of Trefftz method and relations to error estimation of finite element approximations - Ohnimus, Stephan; Rüter, Marcus; Stein, Erwin (Computer Assisted Methods in Engineering and Science, 2023)
In this paper a guaranteed upper bound of the global discretization error in linear elastic finite element approximations is presented, based on a generalized Trefftz functional. Therefore, the general concept of complementary energy functionals and the corresponding approximation methods of Ritz, Trefftz, the method of orthogonal projection and the hypercircle method are briefly outlined. Furthermore, it is shown how to use a generalized Trefftz functional to solve a Neumann problem in linear elasticity. Based on an implicit a posteriori error estimator within the finite element method, using equilibrated local Neumann problems, the generalized Trefftz functional yields a computable guaranteed upper bound of the discretization error without multiplicative constants.