On the H1-stability of the L2-projection onto finite element spaces
نویسندگان
چکیده
We study the stability in the H1-seminorm of the L2-projection onto finite element spaces in the case of nonuniform but shape regular meshes in two and three dimensions and prove, in particular, stability for conforming triangular elements up to order twelve and conforming tetrahedral elements up to order seven.
منابع مشابه
Merging the Bramble-Pasciak-Steinbach and the Crouzeix-Thomée criterion for H1-stability of the L2-projection onto finite element spaces
Suppose S ⊂ H1(Ω) is a finite-dimensional linear space based on a triangulation T of a domain Ω, and let Π : L2(Ω) → L2(Ω) denote the L2-projection onto S. Provided the mass matrix of each element T ∈ T and the surrounding mesh-sizes obey the inequalities due to Bramble, Pasciak, and Steinbach or that neighboring element-sizes obey the global growth-condition due to Crouzeix and Thomée, Π is H1...
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Suppose S ⊂ H1(Ω) is a finite-dimensional linear space based on a triangulation T of a domain Ω, and let Π : L2(Ω) → L2(Ω) denote the L2-projection onto S. Provided the mass matrix of each element T ∈ T and the surrounding mesh-sizes obey the inequalities due to Bramble, Pasciak, and Steinbach or that neighboring element-sizes obey the global growth-condition due to Crouzeix and Thomée, Π is H1...
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عنوان ژورنال:
- Numerische Mathematik
دوره 126 شماره
صفحات -
تاریخ انتشار 2014