×
Babuška, Ivo; Osborn, J.

Analysis of finite element methods for second order boundary value problems using mesh dependent norms. (English) Zbl 0404.65055

Numer. Math. 34, 41-62 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0404.65055

Cited in 2 Reviews
Cited in 26 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65N15 Error bounds for boundary value problems involving PDEs

Keywords:

New Approach; Analysis of Finite Element Methods; Approximate Solution; Boundary Value Problems; Sobolev Norm Estimates; Ritz-Galerkin; Approximation; Stability; Partial Differential Equations of Elliptic Type; L2-Space-Norm Estimates
PDFBibTeX XMLCite
\textit{I. Babuška} and \textit{J. Osborn}, Numer. Math. 34, 41--62 (1980; Zbl 0404.65055)
Full Text: DOI EuDML

References:

[1] Babuška, I.: Error-bounds for finite element method. Numer. Math.16, 322–333 (1971) · Zbl 0214.42001 · doi:10.1007/BF02165003
[2] Babuška, I., Aziz, A.K.: Survey Lectures on the Mathematical Foundation of the Finite Element Method. In: The mathematical foundations of the finite element method with applications to partial differential equations, A.K. Aziz, ed. pp. 5–359, New York: Academic 1973
[3] Boor, C. de: The Method of projections as applied to the numerical solution of two point boundary value problems using cubic splines. Thesis, University of Michigan, 1966
[4] Bramble, J., Hilbert, S.: Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation. SIAM J. Numer. Anal.,13, 185–197 (1976) · Zbl 0334.76010 · doi:10.1137/0713019
[5] Douglas, J., Jr., Dupont, T., Wahlbin, L.: OptimalL error estimates for Galerkin approximations to solutions of two-point boundary value problems. Math. Comp.29, 475–483 (1975) · Zbl 0306.65053
[6] Eisenstat, S., Schreiber, R., Schultz, M.: On the optimality of the Rayleigh-Ritz approximation. Research Report #83, Dept. of Computer Science, Yale University, New Haven
[7] Natterer, F.: Uniform convergence of Galerkin’s method for splines on highly nouniform meshes. Math. Comp.31, 457–468 (1977) · Zbl 0359.65076
[8] Nečas, J.: Les méthodes directes en théorie des équations elliptiques. Paris: Masson 1967
[9] Nitsche, J.: Ein Kriterium für die Quasi-Optimalität des Ritzschen Verfahrens. Numer. Math.11, 346–348 (1968) · Zbl 0175.45801 · doi:10.1007/BF02166687
[10] Nitsche, J.:L convergence of finite element approximations. Proceedings of Symposium on Mathematical Aspects of Finite Element Methods, Rome, 1975
[11] Nitsche, J., Schatz, A.: Interior estimates for Ritz-Galerkin methods. Math. Comp.28, 937–958 (1974) · Zbl 0298.65071 · doi:10.1090/S0025-5718-1974-0373325-9
[12] Schatz, A.: A weak discrete maximum principle and stability of the finite element method inL on plane polygonal domains. I. Math. Comp. (in press 1980) · Zbl 0425.65060
[13] Wheeler, M.: An optimalL error estimate for Galerkin approximations to solutions of two point boundary value problems. SIAM J. Numer. Anal.10, 914–917 (1973) · Zbl 0266.65061 · doi:10.1137/0710077
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.