A novel post-processed finite element method and its convergence for partial differential equations

In this article, by combining high-order interpolation on coarse meshes and low-order finite element solutions on fine meshes, we propose a novel approach to improve the accuracy of the finite element method. The new method is in general suitable for most partial differential equations. For simplicity, we use the second-order elliptic problem as an example to show how the novel approach improves the accuracy of the finite element method. Numerical tests are also conducted to validate the main theoretical results.