Abstract
A new numerical method for 2D linear elliptic partial differential equations in an arbitrary geometry is presented. The special feature of the method presented is that the trial functions, which are used to approximate a solution, satisfy the PDE only approximately. This reduction of the requirement to the trial functions extends the field of application of the Trefftz method. The method is tested on several one-and two-dimensional problems.
References
[1] G.H. Hardy. Divergent Series, Oxford, 1949.
[2] I. Herrera. Trefftz method. In: C.A. Brebbia, ed., Progress in Boundary Element Methods, vol. 3. Wiley, New York,1983.
[3] J. Jirousek, A. Wróblewski. T-elements: State of the art and future trends, Archive of Computational Methods in Engineering, 3/4: 323- 434, 1996.
[4] C. Lanczos. Applied Analysis. Prentice Hall Inc., New York, 1956.
[5] S.A. Lifits, S.Yu. Reutskiy, B. Tirozzi. A new Trefftz-type method for solving boundary value problems. ARI, 50: 85- 95, 1997.
[2] I. Herrera. Trefftz method. In: C.A. Brebbia, ed., Progress in Boundary Element Methods, vol. 3. Wiley, New York,1983.
[3] J. Jirousek, A. Wróblewski. T-elements: State of the art and future trends, Archive of Computational Methods in Engineering, 3/4: 323- 434, 1996.
[4] C. Lanczos. Applied Analysis. Prentice Hall Inc., New York, 1956.
[5] S.A. Lifits, S.Yu. Reutskiy, B. Tirozzi. A new Trefftz-type method for solving boundary value problems. ARI, 50: 85- 95, 1997.
