L2-orthogonal projections onto finite elements on locally refined meshes are H1-stable
L2-orthogonal projections onto finite elements on locally refined meshes are H1-stable
复制标题
局部细化网格上有限元的 L2 正交投影是 H1 稳定的
DOI：
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发表时间：
2013
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. Karkulik;C. Pfeiler;D. Praetorius
我们合并并扩展了最近的结果，证明了 L2 正交投影到标准有限元空间上的 H1 稳定性，前提是基础单纯三角剖分被适当分级。对于 d>=2 的 Rd 中的最低阶 Courant 有限元 S1(T)，我们证明对于由最新顶点二等分生成的自适应网格始终可以确保这样的分级。对于 p>=1 的高阶有限元 Sp(T)，我们通过计算机辅助证明扩展了多项式次数的现有界限。我们还考虑了 Sp(T) 某些子空间上的 L2 正交投影，其中包含零狄利克雷边界条件。积分均值零属性。
We merge and extend recent results which prove the H1-stability of the L2-orthogonal projection onto standard finite element spaces, provided that the underlying simplicial triangulation is appropriately graded. For lowest-order Courant finite elements S1(T) in Rd with d>=2, we prove that such a grading is always ensured for adaptive meshes generated by newest vertex bisection. For higher-order finite elements Sp(T) with p>=1, we extend existing bounds on the polynomial degree with a computer-assisted proof. We also consider L2-orthogonal projections onto certain subspaces of Sp(T) which incorporate zero Dirichlet boundary conditions resp. an integral mean zero property.