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Maximum norm stability and error estimates in parabolic finite element equations. (English) Zbl 0414.65066


MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
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[1] Agmon, Comm. Pure Appl. Math. 15 pp 119– (1962)
[2] Agmon, Comm. Pure Appl. Math. 12 pp 623– (1959)
[3] Baker, Math. Comp. 31 pp 818– (1977)
[4] , and , Partial Differential Equations, Wiley-Interscience, New York, 1964.
[5] Approximate solution of elliptic and parabolic boundary value problems, Thesis, University of California, Berkeley, 1970.
[6] Bramble, SIAM J. Numer. Anal. 14 pp 218– (1977)
[7] Brenner, SIAM J. Numer. Anal. 16 pp 683– (1979)
[8] The Finite Element Method for Elliptic Problems, North Holland, Amsterdam, 1978.
[9] Descloux, SIAM J. Numer. Anal. 9 pp 260– (1972)
[10] Dobrowolski, SIAM J. Numer. Anal.
[11] Douglas, Numer. Math. 23 pp 193– (1975)
[12] Frehse, Bonn. Math. Schr. 89 pp 92– (1976)
[13] Partial Differential Equations, Holt, Reinhardt and Winston, New York, 1969.
[14] Helfrich, Manuscripta Math. 13 pp 219– (1974)
[15] John, Comm. Pure Appl. Math. 5 pp 155– (1952)
[16] L/infty-convergence of finite-element approximations, Mathematical Aspects of Finite Element Methods, Lecture Notes in Math. 606, Springer, New York, 1977, pp. 261–274.
[17] Nitsche, RAIRO Anal. Numér. 13 pp 31– (1979)
[18] Semi-Groups of Linear Operators and Applications to Partial Differential Equations, Dept. of Math., University of Maryland, 1974.
[19] Rannacher, Math. Z. 149 pp 69– (1976)
[20] Schatz, Math. Comp. 34 pp 77– (1980)
[21] and , On the quasi-optimality in L/infty of the H1 projection into finite element spaces, to appear.
[22] Thomée, Math. Comp. 28 pp 1– (1974)
[23] Wahlbin, RAIRO Anal. Numer. 12 pp 173– (1978)
[24] A remark on parabolic smoothing and the finite-element method, SIAM J. Numer. Anal., Feb. 1980. · Zbl 0445.65104
[25] Wheeler, SIAM J. Numer. Anal. 10 pp 723– (1973)
[26] Yosida, Proc. Jn. Acad. 34 pp 337– (1958)
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