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- W2080991003 abstract "The aim of the paper is to show the stability of the finite element solution for the Stokes system in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper W Subscript normal infinity Superscript 1> <mml:semantics> <mml:msubsup> <mml:mi>W</mml:mi> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> <mml:mn>1</mml:mn> </mml:msubsup> <mml:annotation encoding=application/x-tex>W^1_infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula> norm on general convex polyhedral domain. In contrast to previously known results, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper W Subscript r Superscript 2> <mml:semantics> <mml:msubsup> <mml:mi>W</mml:mi> <mml:mi>r</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:annotation encoding=application/x-tex>W^2_r</mml:annotation> </mml:semantics> </mml:math> </inline-formula> regularity for <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=r greater-than 3> <mml:semantics> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>></mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>r>3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, which does not hold for general convex polyhedral domains, is not required. The argument uses recently available sharp Hölder pointwise estimates of the corresponding Green’s matrix together with novel local energy error estimates, which do not involve an error of the pressure in a weaker norm." @default.
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- W2080991003 date "2012-03-01" @default.
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- W2080991003 title "Pointwise error estimates of finite element approximations to the Stokes problem on convex polyhedra" @default.
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