Local piecewise polynomial curve of variable order and its appliance for calculating of nodal derivatives

The nodal basis of $C^m$-$P_{k}^{(3)}$ and $C^m$-$P_{k}^{(4)}$ finite elements on tetrahedral and 4D simplicial grids

We construct the nodal basis of $C^m$-$P_{k}^{(3)}$ ($k \ge 2^3m+1$) and $C^m$-$P_{k}^{(4)}$ ($k \ge 2^4m+1$) finite elements on 3D tetrahedral and 4D simplicial grids, respectively. $C^m$-$P_{k}^{(n)}$ stands for the space of globally $C^m$ ($m\ge1$) and locally piecewise $n$-dimensional polynomials of degree $k$ on $n$-dimensional simplicial grids. We prove the uni-solvency and the $C^m$ continuity of the constructed $C^m$-$P_{k}^{(3)}$ and $C^m$-$P_{k}^{(4)}$ finite element spaces. A computer code is provided which generates the index set for the nodal basis of $C^m$-$P_k^{(n)}$ finite elem…

低阶拟态有限差分方法

On low order mimetic finite difference methods

本文回顾了两类低阶拟态有限差分方法（混合型与节点型），通过比较揭示其构造的相似性，并提出了节点型方法的逐段线性后处理。

广义Ritz-Galerkin有限元近似在二阶椭圆问题中的超收敛性

Superconvergence of Ritz-Galerkin Finite Element Approximations for Second Order Elliptic Problems

本文推导了二阶椭圆方程-∇·(A∇u)=f在Dirichlet边界条件下的广义Ritz-Galerkin有限元近似O(h⁴)超收敛性，基于A-等边假设条件，通过数值实验验证了超收敛理论。