论文信息 - The cracked-beam problem solved by the boundary approximation method

The cracked-beam problem solved by the boundary approximation method

Abstract The cracked-beam problem, as a variant of Motz’s problem, is discussed, and its very accurate solution in double precision is explicitly provided by the boundary approximation method (BAM) (i.e., the Trefftz method). Half of its expansion coefficients are zero, which is supported by an a posteriori analysis. Finding a good model of singularity problems is important for studying numerical methods. As a singularity model, the cracked-beam problem given in this paper seems to be superior to Motz’s problem in Li et al. [Z.C. Li, R. Mathon, P. Serman, Boundary methods for solving elliptic problem with singularities and interfaces, SIAM J. Numer. Anal. 24 (1987) 487–498].

T. T. Lu | Z. C. Li

[1] P. G. Ciarlet,et al. Basic error estimates for elliptic problems , 1991 .

[2] G. Fix,et al. On the use of singular functions with finite element approximations , 1973 .

[3] T. Lu,et al. Singularities and treatments of elliptic boundary value problems , 2000 .

[4] G. Strang,et al. An Analysis of the Finite Element Method , 1974 .

[5] Lorraine G. Olson,et al. An efficient finite element method for treating singularities in Laplace's equation , 1991 .

[6] J. Barkley Rosser,et al. A Power Series Solution of a Harmonic Mixed Boundary Value Problem. , 1975 .

[7] Ivo Babuška,et al. The method of auxiliary mapping for the finite element solutions of elasticity problems containing singularities , 1993 .

[8] H. Motz,et al. The treatment of singularities of partial differential equations by relaxation methods , 1947 .

[9] Rudolf Mathon,et al. Boundary methods for solving elliptic problems with singularities and interfaces , 1987 .

[10] Lorraine G. Olson,et al. A SINGULAR FUNCTION BOUNDARY INTEGRAL METHOD FOR THE LAPLACE EQUATION , 1996 .