×

zbMATH — the first resource for mathematics

Interior and superconvergence estimates for mixed methods for second order elliptic problems. (English) Zbl 0613.65110
Es werden gemischte Finite-Element-Methoden zur numerischen Behandlung von linearen und quasilinearen elliptischen Randwertproblemen untersucht. Nach Gewinnung lokaler Fehlerabschätzungen in Sobolev-Räumen mit nichtpositivem Index werden entsprechende Abschätzungen für Differenzenquotienten der Fehler sowie Superkonvergenzaussagen hergeleitet.
Reviewer: F.v.Finckenstein

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
35J65 Nonlinear boundary value problems for linear elliptic equations
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] [1] J. H. BRAMBLE and A. H. SCHATZ, Estimates for spline projections, R.A.I.R.O., Anal. numér., 10 (1976), pp. 5-37. Zbl0343.65045 MR436620 · Zbl 0343.65045
[2] Higher order local accuracy by averaging in the finite element method, Math, of Comp., 31 (1977), pp. 94-111. Zbl0353.65064 MR431744 · Zbl 0353.65064
[3] J. Jr. DOUGLAS, and J. E. ROBERTS, Global estimates for mixed methods for secondorder elliptic problems, Math, of Comp., 44 (1985), pp. 39-52. Zbl0624.65109 MR771029 · Zbl 0624.65109
[4] J. L. LIONS and E. MAGENES, Non homogeneous boundary value problems and applications, I, Springer-Verlag, Berlin, 1970. Zbl0223.35039 · Zbl 0223.35039
[5] F. A. MILNER, Mixed finite element methods for quasi linear second order elliptic problems, Math, of Comp., 44 (1985), pp. 303-320. Zbl0567.65079 MR777266 · Zbl 0567.65079
[6] [6] J. C. NEDELEC, Mixed finite elements in R 3 , Numer. Math., 35 (1980), pp. 315-341. Zbl0419.65069 MR592160 · Zbl 0419.65069
[7] J. A. NITSCHE and A. H. SCHATZ, Interior estimates for Ritz-Galerkin methods, Math, of Comp., 28 (1974), pp. 937-958. Zbl0298.65071 MR373325 · Zbl 0298.65071
[8] P. A. RAVIART and J. M. THOMAS, A mixed finite element method for 2nd order elliptic problems, in Proceedings of a Conference on Mathematical Aspects of Finite Element Methods, Lecture Notes in Mathematics 606, Springer-Verlag, Berlin, 1977, pp. 292-315. Zbl0362.65089 MR483555 · Zbl 0362.65089
[9] [9] R. SCHOLZ, L \infty -convergence of saddle-point approximations for second order problems, R.A.I.R.O., Anal, numér., 11 (1977), pp. 209-216. Zbl0356.35026 MR448942 · Zbl 0356.35026
[10] G. STAMPACCHIA, Equations elliptiques du second ordre à coefficients discontinus, Les Presses de l’Université de Montréal, Montréal, 1966. Zbl0151.15501 MR251373 · Zbl 0151.15501
[11] J. M. THOMAS, Sur l’analyse numérique des méthodes d’éléments finis hybrides et mixtes,Université P.-et-M. Curie, Paris, 1977.
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.