Some new error estimates for Ritz–Galerkin methods with minimal regularity assumptions
- 1 January 1996
- journal article
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 65 (213) , 19-27
- https://doi.org/10.1090/s0025-5718-96-00649-7
Abstract
New uniform error estimates are established for finite element approximations of solutions of second-order elliptic equations using only the regularity assumption . Using an Aubin--Nitsche type duality argument we show for example that, for arbitrary (fixed) sufficiently small, there exists an such that forKeywords
This publication has 8 references indexed in Scilit:
- Convergence Analysis of the Schwarz Algorithm and Multilevel Decomposition Iterative Methods II: Nonselfadjoint and Indefinite Elliptic ProblemsSIAM Journal on Numerical Analysis, 1993
- Multiplicative Schwarz Algorithms for Some Nonsymmetric and Indefinite ProblemsSIAM Journal on Numerical Analysis, 1993
- Convergence Analysis of Multigrid Algorithms for Nonselfadjoint and Indefinite Elliptic ProblemsSIAM Journal on Numerical Analysis, 1993
- Iterative Schemes for Nonsymmetric and Indefinite Elliptic Boundary Value ProblemsMathematics of Computation, 1993
- Domain Decomposition Algorithms for Indefinite Elliptic ProblemsSIAM Journal on Scientific and Statistical Computing, 1992
- Nonuniform Error Estimates for the Finite Element MethodSIAM Journal on Numerical Analysis, 1975
- An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear FormsMathematics of Computation, 1974
- Constructive proofs of representation theorems in separable Hilbert spaceCommunications on Pure and Applied Mathematics, 1964