The continuous Galerkin finite element methods for linear neutral delay differential equations

摘要

In the paper, the superconvergence of continuous Galerkin finite element methods (CGFEMs) for linear delay differential equations of neutral type is presented. By the orthogonal analysis method and under the suitable condition, it is proven that the finite element solution is superconvergent at the nodal points and Lobatto points. Numerical experiments further confirm the effectiveness and the superconvergence of the CGFEMs.