Ultraconvergence of the derivative of high-order finite element method for elliptic problems with constant coefficients |
| |
Authors: | Wenming He |
| |
Affiliation: | Department of Mathematics, Lingnan Normal University, Zhanjiang, China |
| |
Abstract: | In this article, for second order elliptic problems with constant coefficients, the local ultraconvergence of the derivative of finite element method using piecewise polynomials of degrees k (k ≥ 2) is studied by the interpolation postprocessing technique. Under suitable regularity and mesh conditions, we prove that at an interior vertex, which is away from the boundary with a fixed distance, the gradient of the postprecessed finite element solution using piecewise polynomials of degrees k (k ≥ 2) converges to the gradient of the exact solution with order . Numerical experiments are used to illustrate our theoretical findings. |
| |
Keywords: | constant coefficients derivative recovery operator interpolation operator theory on local mesh symmetry |
|
|