Convergence of Adaptive FEM for some Elliptic Obstacle Problem with Inhomogeneous Dirichlet Data
Convergence of Adaptive FEM for some Elliptic Obstacle Problem with Inhomogeneous Dirichlet Data
复制标题
自适应有限元法求解非齐次狄利克雷数据椭圆障碍问题
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
D. Praetorius
中科院分区：
文献类型：
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作者：
M. Feischl;M. Page;D. Praetorius
M.FEISCHL、M.PAGE和D.pretoriumabstract.在这项工作中，我们证明了具有全局ffiNe障碍和非齐次Dirichlet数据的椭圆障碍问题的自适应最低阶有限元的收敛。自适应回路由Bar-tels，Carstensen&Hoppe(2007)中引入的基于残差的误差刺激器控制，该误差刺激器也被扩展以控制Dirichletdata的振荡。本着Cascon等人的精神。(2008)，我们证明了能量误差、估计量和Dirichlet振荡的加权和满足fi压缩性质，直到一定的能量贡献。这一结果将Bartels，Carstensen&Hoppe(2007)和Page&Praetorius(2009)的分析推广到非齐次Dirichletdata的情形，并引入了一些能量估计来克服离散空间嵌套的不足。一个简短的结论说明了afem关于非affine障碍的问题。
M. FEISCHL, M. PAGE, AND D. PRAETORIUSAbstract. In this work, we show the convergence of adaptive lowest-order FEM (AFEM)for an elliptic obstacle problem with globally affine obstacle and non-homogeneous Dirichletdata. The adaptive loop is steered by some residual based errorestimator introduced in Bar-tels, Carstensen & Hoppe (2007) that is extended to control oscillations of the Dirichletdata, as well. In the spirit of Cascon et al. (2008), we show that a weighted sum of energyerror, estimator, and Dirichlet oscillations satisfies a contraction property up to certain van-ishing energy contributions. This result extends the analysis of Bartels, Carstensen &Hoppe (2007) and Page & Praetorius (2009) to the case of non-homogeneous Dirichletdata and introduces some energy estimates to overcome the lack of nestedness of the discretespaces. A short conclusion adresses AFEM for problems with non-affine obstacles.