Linear differential operators on bivariate spline spaces and spline vector fields

DOI10.1007/s10543-015-0557-xzbMath1342.41010OpenAlexW1994235751MaRDI QIDQ285262

Tatyana Sorokina, Peter Alfeld

Publication date: 19 May 2016

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-015-0557-x

zbMATH Keywords

finite elementBernstein-Bézier techniquesspline vector field

Mathematics Subject Classification ID

Numerical interpolation (65D05) Spline approximation (41A15)

Related Items (12)

Generalized finite element systems for smooth differential forms and Stokes' problem ⋮ Divergence-free quasi-interpolation ⋮ An interpolated Galerkin finite element method for the Poisson equation ⋮ Bernstein-Bézier techniques for divergence of polynomial spline vector fields in \(\mathbb{R}^n\) ⋮ A characterization of supersmoothness of multivariate splines ⋮ Mini-workshop: Interpolation, approximation, and algebra. Abstracts from the mini-workshop held February 13--19, 2022 ⋮ Inf-Sup Stable Finite Elements on Barycentric Refinements Producing Divergence--Free Approximations in Arbitrary Dimensions ⋮ An inequality involving a triangle and an interior point and its application ⋮ Conforming and nonconforming harmonic finite elements ⋮ Trivariate interpolated Galerkin finite elements for the Poisson equation ⋮ Unnamed Item ⋮ The Stokes complex: A review of exactly divergence–free finite element pairs for incompressible flows

Uses Software

• MDS

Cites Work

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• Geometric decompositions and local bases for spaces of finite element differential forms
• Intrinsic supersmoothness of multivariate splines
• A stable finite element for the Stokes equations
• Mixed finite elements for elasticity on quadrilateral meshes
• Redundancy of smoothness conditions and supersmoothness of bivariate splines
• Spline Functions on Triangulations
• Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials
• Piecewise Quadratic Approximations on Triangles
• A new family of stable mixed finite elements for the 3D Stokes equations
• Piecewise polynomials and the finite element method

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