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Ewing, R. E.

Efficient multistep procedures for nonlinear parabolic problems with nonlinear Neumann boundary conditions. (English) Zbl 0522.65072

Calcolo 19, 231-252 (1982).
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Cited in 3 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N40 Method of lines for boundary value problems involving PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations

Keywords:

multistep procedures; time-stepping Galerkin methods; nonlinear Neumann boundary conditions; preconditioned iterative method; optimal order convergence rates
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\textit{R. E. Ewing}, Calcolo 19, 231--252 (1982; Zbl 0522.65072)
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References:

[1] O. Axelsson,On preconditioning and convergence acceleration in space matrix problems, CERN European Organization for Nuclear Research, Geneva, 1974.
[2] J. H. Bramble,Multistep methods for quasilinear equations, Computational Methods in Nonlinear Mechanics J. T. Oden, editor, North Holland Publishing Company, New York (1980). · Zbl 0428.73083
[3] J. H. Bramble, R. E. Ewing,Efficient starting procedures for high order time-stepping methods for differential equations (to appear).
[4] J. H. Bramble, R. E. Ewing Alternating direction multistep methods for parabolic problems-iterative stabilization, (to appear). · Zbl 0686.65078
[5] J. H. Bramble, R. E. Ewing,Direct alternating direction multistep methods for parabolic problems, (to appear). · Zbl 0686.65078
[6] J. H. Bramble, P. H. Sammon,Efficient higher order single-step methods for parabolic problems: part I, Math. Res. Center Rep. #1958, Madison, Wisconsin (1979) and Math. Comp. (to appear). · Zbl 0476.65072
[7] J. H. Bramble, P. H. Sammon,Efficient higher order multistep methods for parabolic problems: part I, (to appear). · Zbl 0476.65072
[8] J. Douglas, Jr., T. Dupont.Galerkin methods for parabolic equations with nonlinear boundary conditions, Numer. Math.20 (1973), 213–237. · Zbl 0234.65096
[9] J. Douglas, Jr., T. Dupont, R. E. Ewing,Incomplete iteration for time-stepping a Galerkin method for a quasilinear parabolic problem, SIAM J. Numer. Anal.16 (1979), 503–522. · Zbl 0411.65064
[10] R. E. Ewing,Time-stepping Galerkin methods for nonlinear Sobolev partial differential equations. SIAM J. Numer. Anal.15 (1978), 1125–1150. · Zbl 0399.65083
[11] R. E. Ewing,Efficient time-stepping methods for miscible displacement problems with nonlinear boundary conditions, Math. Res. Center Rep. #1952, Madison, Wisconsin (1979).
[12] R. E. Ewing,On efficient time-stepping methods for monlinear partial differential equations, Comput. Math. Appl.6 (1980) 1–13. · Zbl 0508.65050
[13] R. Ewing, T. F. Fussell,Efficient time-stepping procedures for miscible displacement problems in porous media, SIAM J. Numer. Anal.19 (1982), 1–67. · Zbl 0498.76084
[14] C. W. Gear,Numerical initial value problems in ordinary differential equations, (1971), Prentice-Hall, New Jersey. · Zbl 1145.65316
[15] P. Henrici,Discrete variable methods in ordinary differential equations (1962), John Wiley and Sons, New York. · Zbl 0112.34901
[16] L. Lions, E. Magenes,Non-homogeneous boundary value problems and applications, I, (1972), Springer-Verlag, New York. · Zbl 0223.35039
[17] M. Luskin,A Galerkin method for nonlinear parabolic equations with nonlinear boundary conditions, SIAM J. Numer. Anal.16 (1979) 284–299. · Zbl 0405.65059
[18] M. F. Wheeler A priori L 2-error estimates for Galerkin approximations to parabolic partial differential equations, SIAM J. Numer. Anal.10 (1973), 723–759. · Zbl 0258.35041
[19] M. Zlámal,Finite element multistep discretizations of parabolic boundary value problems, Math. Comput.29 (1975) 350–359. · Zbl 0302.65081
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