EACH H1/2-STABLE PROJECTION YIELDS CONVERGENCE AND QUASI-OPTIMALITY OF ADAPTIVE FEM WITH INHOMOGENEOUS DIRICHLET DATA IN Rd
EACH H1/2-STABLE PROJECTION YIELDS CONVERGENCE AND QUASI-OPTIMALITY OF ADAPTIVE FEM WITH INHOMOGENEOUS DIRICHLET DATA IN Rd
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DOI：
10.1051/m2an/2013069
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发表时间：
2013-07-01
期刊：
影响因子：
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通讯作者：
Praetorius, D.
中科院分区：
文献类型：
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作者：
Aurada, M.;Feischl, M.;Praetorius, D.
本文考虑了具有固定多项式阶数p - epsilon n的R-d中二阶非齐次Dirichlet数据的椭圆型偏微分方程的h-自适应有限元解法。作为模型实例，服务于具有混合Dirichlet- neumann边界条件的泊松方程，其中非齐次Dirichlet数据采用h- 1/2稳定投影进行离散，例如p = 1时的l -2投影或一般p >= 1时的Scott-Zhang投影。对于误差估计，我们使用包含狄利克雷数据振荡的残差估计量。证明了每一个h -1/2稳定投影即使具有拟最优收敛速率，也具有自适应算法的收敛性。采用Scott-Zhang投影的数值实验对工作进行了总结。
We consider the solution of second order elliptic PDEs in R-d with inhomogeneous Dirichlet data by means of an h-adaptive FEM with fixed polynomial order p epsilon N. As model example serves the Poisson equation with mixed Dirichlet-Neumann boundary conditions, where the inhomogeneous Dirichlet data are discretized by use of an H-1/2-stable projection, for instance, the L-2-projection for p = 1 or the Scott-Zhang projection for general p >= 1. For error estimation, we use a residual error estimator which includes the Dirichlet data oscillations. We prove that each H-1/2-stable projection yields convergence of the adaptive algorithm even with quasi-optimal convergence rate. Numerical experiments with the Scott-Zhang projection conclude the work.