Superconvergence of Modified Nonconforming Cut Finite Element Method for Elliptic Problems

In this work, we aim to explore the superconvergence of a modified nonconforming cut finite element method with rectangular meshes for elliptic problems. Boundary conditions are imposed via the Nitsche’s method. The superclose property is proven for rectangular meshes. Moreover, a postprocessing interpolation operator is introduced, and it is proven that the postprocessed discrete solution converges to the exact solution, with a superconvergence rate O(h3/2). Finally, numerical examples are provided to support the theoretical analysis.