The cracked-beam problem solved by the boundary approximation method

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].