Self-adaptive Trefftz procedure for harmonic problems - Kołodziej, Jan A.; Starosta, Roman (Computer Assisted Methods in Engineering and Science, 2023)
The paper propose two adaptive algorithms based on a Trefftz method for two-dimensional Laplace equation satisfying the maximal principle. First one for given the error tolerance and an initial number of terms in the solution expansion, the algorithm computes expansion coefficient by location of boundary conditions and evaluates the maximum absolute error on the boundary. If error exceeds the error the tolerance, additional expansion terms and boundary collocation points are added and process repeated until the tolerance is satisfied. The second one is based on Galerkin formulation of Trefftz method and utilizes the exact potential error norm for predict a new mesh and new solution expansion until the tolerance is satisfied.