A Cut Finite Element Method with Boundary Value Correction

摘要: In this contribution we develop a cut finite element method with boundary value correction of the type originally proposed by Bramble, Dupont, and Thomee. The is fictitious domain Nitsche enforcement Dirichlet conditions together stabilization elements at which stable enjoy optimal order approximation properties. A computational difficulty is, however, geometric computations related to quadrature on must be accurate enough achieve higher approximation. With may use only piecewise linear boundary, very convenient in method, still obtain convergence. modified formulation involving Taylor expansion normal direction compensating for boundary. Key analysis consistent term enables us prove stability priori error estimates explicit dependence meshsize distance between exact approximate