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Maximum-norm-stability and error-estimates in Galerkin methods for parabolic equations in one space variable. (English) Zbl 0515.65082

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
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[1] Babu?ka, I., Osborn, J.: Analysis of finite element methods for second order boundary value problems using mesh dependent norms. Numer. Math.34, 41-62 (1980) · Zbl 0404.65055 · doi:10.1007/BF01463997
[2] DeBoor, C., Fix, G.J.: Spline approximation by quasiinterpolants. J. Approximation Theory8, 19-45 (1973) · Zbl 0279.41008 · doi:10.1016/0021-9045(73)90029-4
[3] Descloux, J.: On finite element matrices. SIAM J. Numer. Anal.9, 260-265 (1972) · Zbl 0242.15009 · doi:10.1137/0709025
[4] Dobrowolski, M.: ZurL ?-Konvergenz finiter Elemente bei parabolischen Differentialgleichungen. Math. Methods Appl. Sci.2, 221-234 (1980) · Zbl 0434.65088 · doi:10.1002/mma.1670020208
[5] Dobrowolski, M.:L ?-convergence of linear finite element approximation to nonlinear parabolic problems. SIAM J. Numer. Anal.17, 663-674 (1980) · Zbl 0449.65077 · doi:10.1137/0717056
[6] Douglas, J., Jr., Dupont, T., Wahlbin, L.B.: OptimalL ? error estimates for Galerkin approximations to solutions of two-point boundary value problems. Math. Comput.29, 475-483 (1975) · Zbl 0306.65053
[7] Friedman, A.: Partial Differential Equations of Parabolic Type. Englewood Cliffs: Prentice-Hall 1964 · Zbl 0144.34903
[8] Friedman, A.: Partial Differential Equations. New York: Rinehart and Winston, 1969 · Zbl 0224.35002
[9] Krein, S.G., Petunin, Y.I.: Scales of Banach spaces. Russian Math. Surveys21, 85-160 (1966) · Zbl 0173.15702 · doi:10.1070/RM1966v021n02ABEH004151
[10] Lions, J.L., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications I. Berlin, Heidelberg, New York: Springer 1972 · Zbl 0223.35039
[11] Nitsche, J.A.:L ?-convergence of finite element approximation. 2. Conference on Finite Elements, Rennes, France, May 12-14, 1975
[12] Nitsche, J.A.:L ?-convergence of finite-element Galerkin approximations on parabolic problems. RAIRO Anal. Numér.13, 31-54 (1979) · Zbl 0401.65069
[13] Schatz, A.H., Thomée, V., Wahlbin, L.B.: Maximum norm stability and error estimates in parabolic finite element equations. Comm. Pure Appl. Math.33, 265-304 (1980) · Zbl 0429.65103 · doi:10.1002/cpa.3160330305
[14] Schreiber, R.: Finite element methods of high-order accuracy for singular two-point boundary value problems with nonsmooth solutions. SIAM J. Numer. Anal.17, 547-566 (1980) · Zbl 0474.65062 · doi:10.1137/0717047
[15] Thomée, V.: Spline approximation and difference schemes for the heat equation. The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations. Aziz, A.K. (ed.), pp. 711-746. New York: Academic Press 1972
[16] Thomée, V.: Some convergence results for Galerkin methods for parabolic boundary value problems. Mathematical Aspects of Finite Elements in Partial Differential Equations. DeBoor, C. (ed.), pp. 55-88. New York: Academic Press 1974
[17] Wahlbin, L.B.: A quasioptimal estimate in piecewise polynomial Galerkin approximation of parabolic problems. Numerical Analysis. Watson, G.A. (ed.), pp. 230-245. Berlin, Heidelberg, New York: Springer Lecture Notes in Mathematics 912, 1982 · Zbl 0515.65083
[18] Wheeler, M.F.:L ? estimates of optimal orders for Galerkin methods for one dimensional second order parabolic and hyperbolic equations. SIAM J. Numer. Anal.10, 908-913 (1973) · Zbl 0266.65074 · doi:10.1137/0710076
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