×

zbMATH — the first resource for mathematics

Direct and inverse error estimates for finite elements with mesh refinements. (English) Zbl 0423.65057

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Babuška, I.: Finite element method for domains with corners. Computing6, 264–273 (1970) · Zbl 0224.65031 · doi:10.1007/BF02238811
[2] Babuška, I., Kellogg, R.B.: Nonuniform error for the finite element method SIAM J. Numer. Anal.12, 868–875 (1975) · Zbl 0339.65062 · doi:10.1137/0712064
[3] Babuška, I., Rosenzweig, M.R.: A finite element scheme for domains with corners. Numer. Math.20, 1–21 (1972) · Zbl 0252.65084 · doi:10.1007/BF01436639
[4] Bergh, J., Löfstrom, J.: Interpolation Spaces. Berlin, Heidelberg, New York: Springer: 1976
[5] Ciarlet, P.: The finite element method for elliptic problems. Amsterdam North-Holland: 1978 · Zbl 0383.65058
[6] Fried, I., Yang, S.K.: Best finite element distribution around a singularity. AIAA J.10, 1244–1246 (1972) · doi:10.2514/3.50360
[7] Grisvard, P.: Behavior of the solutions of an elliptic boundary value problem in a polygonal or polyhedral domain. In: Numerical Solution of Partial Differential Equation–III, Hubbard, B. ed pp. 207–274. New York: Academic Press 1976 · Zbl 0361.35022
[8] Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities, 2nd ed., Cambridge: Cambridge Univ. Press 1952
[9] Kondrat’ev, V.A.: Boundary problems for elliptic equations with conical or angular points. Trans. Moscow Math Soc.16, 227–313 (1967) · Zbl 0194.13405
[10] Raugel, G.: Résolution numérique de problemes elliptiques dans des domains avec coins. Thesis, University of Rennes, 1978
[11] Schatz, A., Wahlbin, L.: Maximum norm estimates in the finite element method on plane polygonal domains, Part 1. Math of Comp.32, 73–109 (1978) · Zbl 0382.65058
[12] Schatz, A., Wahlbin, L.: Maximum norm estimates in the finite element method on plane polygonal domains, Part II. Math. Comput.33, 465–492 (1979) · Zbl 0417.65053
[13] Stein, E.: Singular integrals and differentiability properties of functions. Princeton: Princeton University Press, 1970 · Zbl 0207.13501
[14] Wait, R., Mitchell, A.R.: Corner singularities in elliptic problems by finite element methods. J. Comp. Physics8, 45–52 (1971) · Zbl 0224.65030 · doi:10.1016/0021-9991(71)90033-7
[15] Whiteman, J.R., Barnhill, R.L.: Finite element methods for elliptic boundary value problems. Proc. Equadiff 3, Czechoslovak Conf. on Diff. Eqns., Brno, Czechoslovakia · Zbl 0284.65087
[16] Widlund, O.: On best error bounds for approximation by piecewise polynomial functions. Numer. Math.27, 327–338 (1977) · Zbl 0331.41010 · doi:10.1007/BF01396181
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.