Interpolation error estimates in \(W^{1,p}\) for degenerate \(Q_1\) isoparametric elements

DOI10.1007/s00211-006-0018-1zbMath1120.65116OpenAlexW2097518087MaRDI QIDQ2503146

Gabriel Acosta, Gabriel Monzón

Publication date: 14 September 2006

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-006-0018-1

zbMATH Keywords

finite elementsmaximum angle conditioninterpolation error estimatesdouble angle conditionregular decomposition property

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (4)

Sharp geometric requirements in the Wachspress interpolation error estimate ⋮ The minimal angle condition for quadrilateral finite elements of arbitrary degree ⋮ On the Poincaré-Friedrichs inequality for piecewise $H^\{1\}$ functions in anisotropic discontinuous Galerkin finite element methods ⋮ Anisotropic interpolation error estimate for arbitrary quadrilateral isoparametric elements

Cites Work

• An optimal Poincaré inequality for convex domains
• Quadrilateral mesh revisited.
• The interpolation theorem for narrow quadrilateral isoparametric finite elements
• Interpolation theory over curved elements, with applications to finite element methods
• On the Angle Condition in the Finite Element Method
• Estimation of the Interpolation Error for Quadrilateral Finite Elements Which Can Degenerate into Triangles
• The Maximum Angle Condition for Mixed and Nonconforming Elements: Application to the Stokes Equations
• An optimal Poincaré inequality in $L^1$ for convex domains
• Error Estimates for $\Cq_1$ Isoparametric Elements Satisfying a Weak Angle Condition
• Error estimates for some quasi-interpolation operators
• Unnamed Item

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