Optimal 𝐿^{∞} estimates for the finite element method on irregular meshes-Reference-Cited by-同舟云学术

Optimal 𝐿^{∞} estimates for the finite element method on irregular meshes

Published:1976 Issue:136 Volume:30 Page:681-697
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Scott Ridgway

Abstract

Uniform estimates for the error in the finite element method are derived for a model problem on a general triangular mesh in two dimensions. These are optimal if the degree of the piecewise polynomials is greater than one. Similar estimates of the error are also derived in L p {L^p} . As an intermediate step, an L 1 {L^1} estimate of the gradient of the error in the finite element approximation of the Green’s function is proved that is optimal for all degrees.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1976-30-136/S0025-5718-1976-0436617-2/S0025-5718-1976-0436617-2.pdf

Reference27 articles.

1. Survey lectures on the mathematical foundations of the finite element method;Babuška, Ivo,1972

2. Bounds for a class of linear functionals with applications to Hermite interpolation;Bramble, J. H.;Numer. Math.,1970

3. Maximum-norm interior estimates for Ritz-Galerkin methods;Bramble, James H.;Math. Comput.,1975

4. Estimates for spline projections;Bramble, J. H.;Rev. Fran\c{c}aise Automat. Informat. Recherche Op\'{e}rationnelle S\'{e}r.,1976

5. Higher order local accuracy by averaging in the finite element method;Bramble, J. H.,1974

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On pointwise error estimates for Voronoï-based finite volume methods for the Poisson equation on the sphere;Advances in Computational Mathematics;2023-06

2. An Interior Maximum Norm Error Estimate for the Symmetric Interior Penalty Method on Planar Polygonal Domains;Computational Methods in Applied Mathematics;2022-10-06

3. A regularized shallow-water waves system with slip-wall boundary conditions in a basin: theory and numerical analysis;Nonlinearity;2021-12-14