Improved accuracy by adapted mesh-refinements in the finite element method-Reference-Cited by-同舟云学术

Improved accuracy by adapted mesh-refinements in the finite element method

Published:1985 Issue:170 Volume:44 Page:321-343
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Eriksson Kenneth

Abstract

For appropriately adapted mesh-refinements, optimal order error estimates are proved for the finite element approximate solution of the Neumann problem for the second-order elliptic equation L u = δ Lu = \delta , where δ \delta is the Dirac distribution.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1985-44-170/S0025-5718-1985-0777267-3/S0025-5718-1985-0777267-3.pdf

Reference15 articles.

1. Pure and Applied Mathematics, Vol. 65;Adams, Robert A.,1975

2. Error-bounds for finite element method;Babuška, Ivo;Numer. Math.,1970

3. I. Babuška & A. K. Aziz, "Survey lectures on the mathematical foundations of the finite element method," Section 6.3.6 of The Mathematical Foundations of the Finite Element Method with Applications to Parital Differential Equations, (A. K. Aziz, ed.), Academic Press, New York, 1973.

4. Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation;Bramble, J. H.;SIAM J. Numer. Anal.,1970

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

Cited by 26 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. A metric-based adaptive mesh refinement criterion under constrain for solving elliptic problems on quad/octree grids;Journal of Computational Physics;2024-06

2. Projection in negative norms and the regularization of rough linear functionals;Numerische Mathematik;2022-03-21

3. A hybridizable discontinuous Galerkin method for second order elliptic equations with Dirac delta source;ESAIM: Mathematical Modelling and Numerical Analysis;2022-02-14

4. Regularity and finite element approximation for two-dimensional elliptic equations with line Dirac sources;Journal of Computational and Applied Mathematics;2021-09

5. The optimal convergence of finite element methods for the three-dimensional second-order elliptic boundary value problem with singularity;Journal of Mathematical Analysis and Applications;2020-11