Numerical convergence on adaptive grids for control volume methods
Numerical convergence on adaptive grids for control volume methods
复制标题
控制体积方法的自适应网格数值收敛
DOI：
10.1002/num.20280
复制
发表时间：
2008
影响因子：
3.9
通讯作者：
I. Aavatsmark
中科院分区：
文献类型：
--
作者：
S. Khattri;I. Aavatsmark
提出了一种求解二阶椭圆型方程的控制体方法的自适应技术。该离散化方法适用于与电导率张量的主方向对齐的初始笛卡尔网格。用数值方法研究了该方法的收敛行为。对于Sobolev正则性较低的解，所得到的L2收敛阶为势流密度的两个收敛阶和一个流密度收敛阶。与均匀网格相比，自适应网格对线性方程组有更好的约束。测试运行表明，基于纯通量的精化标准是可取的。#2007 Wiley期刊，Inc.Numer方法偏微分公式，2008
An adaptive technique for control‐volume methods applied to second order elliptic equations in two dimensions is presented. The discretization method applies to initially Cartesian grids aligned with the principal directions of the conductivity tensor. The convergence behavior of this method is investigated numerically. For solutions with low Sobolev regularity, the found L2 convergence order is two for the potential and one for the flow density. The system of linear equations is better conditioned for the adaptive grids than for uniform grids. The test runs indicate that a pure flux‐based refinement criterion is preferable.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008