Aspects of Trefftz' Method in BEM and FEM and their coupling
Abstract
In both boundary element methods and Trefftz-type finite element methods a partial differential equation in some domain is treated by solving a discrete problem on the boundary of the domain and possibly the boundaries between subdomains. We consider a Trefftz element formulation which is based on the complementary energy functional, and we compare different regularizations of the interelement continuity conditions. Also starting from the complementary energy functional, mixed finite elements can be constructed such that the stresses satisfy equilibrium a priori. We describe a coupling of these elements with the by now classical symmetric Galerkin-BEM.
References
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[2] D.N. Arnold, F. Brezzi, J . Douglas. PEERS: A new mixed finite element for plane elasticity. Japan J. Appl. Math., 1: 347- 367, 1984.
[3] D. Braess, O. Klaas, R. Niekamp, E. Stein, F. Wobschal. Error indicators for mixed finite elements in 2- dimensional linear elasticity. Comput. Methods Appl. Mech. Engrg., 127: 345-356, 1995.
[4] U. Brink, C. Carstensen, E. Stein. Symmetric coupling of boundary elements and Raviart- Thomas-type mixed finite elements in elastostatics. Numerische Mathematik, 75: 153- 174, 1996.
[5] U. Brink, O. Klaas, R. Niekamp, E. Stein. Coupling of adaptively refined dual mixed finite elements and boundary elements in linear elasticity. Advances in Engineering Software, 24: 13- 26, 1995.
[2] D.N. Arnold, F. Brezzi, J . Douglas. PEERS: A new mixed finite element for plane elasticity. Japan J. Appl. Math., 1: 347- 367, 1984.
[3] D. Braess, O. Klaas, R. Niekamp, E. Stein, F. Wobschal. Error indicators for mixed finite elements in 2- dimensional linear elasticity. Comput. Methods Appl. Mech. Engrg., 127: 345-356, 1995.
[4] U. Brink, C. Carstensen, E. Stein. Symmetric coupling of boundary elements and Raviart- Thomas-type mixed finite elements in elastostatics. Numerische Mathematik, 75: 153- 174, 1996.
[5] U. Brink, O. Klaas, R. Niekamp, E. Stein. Coupling of adaptively refined dual mixed finite elements and boundary elements in linear elasticity. Advances in Engineering Software, 24: 13- 26, 1995.
Published
2023-10-17
Issue
pp. 327-344
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Brink, U., Kreienmeyer, M., Peters, K., & Stein, E. (2023). Aspects of Trefftz’ Method in BEM and FEM and their coupling. Computer Assisted Methods in Engineering and Science, 4(3-4), 327-344. https://cames3.ippt.pan.pl/index.php/cames/article/view/1553
