椭圆方程的最小二乘三角单元Legendre Galerkin数值积分法

Least Squares Triangular Legendre Galerkin with Numerical Integral Method for Elliptic Equations

研究三角形域上椭圆型方程的最小二乘三角单元Legendre Galerkin数值积分法。该方法基于最小二乘原理,在离散时采用Legendre Galerkin数值积分处理,使得格式既有Legendre Galerkin数值积分实施方便的优势,同时又有对应的代数方程的系数矩阵具有的对称正定的特点。对变系数部分的计算,则用Legendre-Gauss-Lobatto (或Chebyshev-Gauss-Lobatto)配置点插值处理。给出数值算例验证格式的谱精度。

The least squares triangular Legendre Galerkin with numerical integration method for elliptic equations is investigated. The method is based on least squares formulation, but Legendre Galerkin with numerical integration is applied to the discretization in time, which combines the advantages of the Legendre Galerkin with numerical integration with the symmetric and positive definite systems being obtained by our scheme. For the calculation of variable coefficients, the Legendre-Gauss-Lobatto (or Chebyshev-Gauss-Lobatto (CGL)) collocation points can be used. Some numerical examples are given to verify the spectral accuracy and effectiveness of the proposed method.