Journal ArticleDOI
Estimation of Linear Functionals on Sobolev Spaces with Application to Fourier Transforms and Spline Interpolation
James H. Bramble,Stephen Hilbert +1 more
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This article is published in SIAM Journal on Numerical Analysis.The article was published on 1970-03-01. It has received 408 citations till now. The article focuses on the topics: Spline interpolation & Interpolation space.read more
Citations
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Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
M. Crouzeix,P.-A. Raviart +1 more
TL;DR: Both conforming and nonconforming finite element methods are studied and various examples of simplicial éléments well suited for the numerical treatment of the incompressibility condition are given.
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ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES
TL;DR: In this paper, the authors studied the stability properties of Isogeometric Analysis in the context of mesh refinement and developed approximation estimates based on a new Bramble-Hilbert lemma in so-called "bent" Sobolev spaces.
Journal ArticleDOI
An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation
Claes Johnson,Juhani Pitkäranta +1 more
TL;DR: In this article, the authors proved Lp stability and error estimates for the discontinuous Galerkin method when applied to a scalar linear hyperbolic equation on a convex polygonal plane domain.
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Finite element exterior calculus: From hodge theory to numerical stability
TL;DR: In this article, the authors consider the numerical discretization of partial differential equations that are related to differential complexes so that de Rham cohomology and Hodge theory are key tools for exploring the well-posedness of the continuous problem.
References
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BookDOI
Multiple integrals in the calculus of variations
TL;DR: In this paper, a variational method in the theory of harmonic integrals has been proposed to solve the -Neumann problem on strongly pseudo-convex manifolds and parametric Integrals two-dimensional problems.
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Piecewise Hermite interpolation in one and two variables with applications to partial differential equations
Journal ArticleDOI
Approximation by periodic spline interpolants on uniform meshes.
TL;DR: In this article, explicit formulas for approximate interpolation, differentiation, integration, and Fourier coefficients, based on interpolation by polynomial splines on uniform meshes, are given.
Journal ArticleDOI
Convergence estimates for essentially positive type discrete Dirichlet problems
TL;DR: In this paper, the authors considered a class of difference approximations to the Dirichlet problem for second-order elliptic operators with smooth coefficients, and showed that the convergence rate is O(hx).