Data oscillation and convergence of adaptive FEM
Data oscillation and convergence of adaptive FEM
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DOI：
10.1137/s0036142999360044
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发表时间：
2000-08-10
影响因子：
2.9
通讯作者：
Siebert, KG
中科院分区：
文献类型：
--
作者：
Morin, P;Nochetto, RH;Siebert, KG
数据振荡是与有限元方法（FEM）相关的平均过程中遗漏的固有信息，而与求积无关。确保数据振荡的减少率，以及基于后验误差估计的误差减少，我们构造了一个简单而有效的自适应有限元椭圆型偏微分方程（PDE）的线性收敛速度没有任何初步的网格适应，也没有明确的知识常数。因此，任何规定的误差容限都是在有限数量的步骤中实现的。二维和三维的许多数值实验产生了准最佳网格，沿着具有竞争力的性能。
Data oscillation is intrinsic information missed by the averaging process associated with finite element methods ( FEM) regardless of quadrature. Ensuring a reduction rate of data oscillation, together with an error reduction based on a posteriori error estimators, we construct a simple and efficient adaptive FEM for elliptic partial differential equations (PDEs) with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants. Any prescribed error tolerance is thus achieved in a finite number of steps. A number of numerical experiments in two and three dimensions yield quasi-optimal meshes along with a competitive performance.