基于外心对偶剖分的有限体积元法

Finite Volume Element Method Based on Circumcenter Dual Subdivisions

考虑基于外心对偶剖分的椭圆型与抛物型方程的有限体积元法.设原始三角形剖分的任意三角形单元的重心Q和外心C的距离满足|QC|=O(h2),在此条件下,证明了二阶椭圆型方程基于外心对偶剖分的有限体积元法的L2误差估计,以及抛物型方程基于外心对偶剖分的半离散和全离散有限体积元格式的L2和H1误差估计.

We considered the finite volume element methods (FVM) based on circumcenter dual subdivision for the elliptic equations and parabolic equations. Let the primal triangular partition satisfy the restrictive condition, that is, the distances between the barycenter Q and the circumcenter C of any triangle element satisfy |QC|=O(h^2), under this condition, firstly we have obtained the optimal L^2 error estimates of the finite (volume) element method based on circumcenter dual subdivision for the elliptic equation, furthermore we have also proved the optimal L^2 and H^1 error estimates of the semi-discrete and fully-discrete finite volume element (method) based on circumcenter dual subdivision for parabolic equation.