A finite element convergence analysis for 3D Stokes equations in case of variational crimes. (Q1581353)

A Stokes problem with mixed boundary conditions is examined in a three-dimensional domain with a piecewise curved boundary. This domain is approximated by a polyhedron which is decomposed into tetrahedra. Then a nonconforming finite element method is applied. This leads to several variational crimes: numerical integration, approximation of the curved boundary, and boundary conditions. The author presents sufficient conditions which guarantee the convergence of discrete solutions to a weak solution of the Stokes problem without any additional regularity assumptions.