Self-adaptive Trefftz procedure for harmonic problems
Abstract
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.
Keywords
References
[1] J. Jirousek, A. Vemkatesh. Adaptivity in HT element formulation. Int. J. Numer. Methods Eng. , 29: 391-405, 1990.[2] Z. Xiaoping, Y. Zhenhan, L. Zhizhong. An adaptive boundary collocation method for plate bending problem. In: B.M. Kwak, M. Tanaka, eds., Computational Engineering, 221- 226, Elsevier Science Publishers, 1993.
[3] W.L. Golik, J.A. Kolodziej. An adaptive boundary collocation method for linear PDEs. Numerical Methods for Partial Differential Equations, 11: 555- 560.
[4] A.C. Mendes, J.A. Kołodziej. An adaptive boundary collocation method for creeping flow between two eccentric cylinders. In: Advances Fluid Mechanics.
[5] E. Kita, N. Kamiya, T. Nomura. H-adaptive scheme for elements-free Trefftz method. In: Proceedings of Boundary Element Technology 96, Hawaii, 1996.
This work is licensed under a Creative Commons Attribution 4.0 International License.