Numerical Analysis of a Biharmonic Boundary Value Problem with a Singularity and Mixed Derivatives in a Generalized Solution

The first boundary value problem for a biharmonic equation in an L-shaped domain is considered. An algorithm for finding an approximate solution to this problem based on Morley’s nonconforming finite element method has been created. Calculations of model boundary value problems with a singularity are carried out. The convergence of the approximate solution to the exact one in the broken norms of the spaces W21Ω, and W22Ω with a fractional exponent of rate order Oh1.1 and Oh0.5, respectively, is numerically confirmed. The behavior of the absolute error in nodes of the triangulation is investigated depending on the decrease of the mesh step h.