D. Estep, An analysis of numerical approximations of metastable solutions of the bistable equation, Nonlinearity, 7 (1994), pp. 1445--1462. Home/Search Document Not in Database Summary Related Articles Check |
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Dynamics Of Lattice Differential Equations - Chow, Mallet-Paret, Van Vleck (Correct)
....because although these types of solutions are not equilibrium solutions their motion is exponentially slow and hence the solution does not change form on very long time scales. In [Grant Van Vleck, 1995] the speed of motion of interfaces for (2) for n = 1 was considered (related work appears in [Estep, 1994]. We summarize here the results that were obtained in [Grand Van Vleck, 1995] They involve first finding bounds on the 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 4 2 0 2 4 Waveform 1 Waveform 2 Waveform 3 Waveform 4 Waveform 5 Fig. 3. Plots of waveforms for ff = 1 2 , c = 0, and various ....
Estep, D. [1994] "An analysis of numerical approximations of metastable solutions of the bistable equation," Nonlinearity 7, 1445--1462.
Slow Motion in Higher-Order Systems and.. - Kalies, VanderVorst.. (1997) (Correct)
....concerning the reliability of such numerical calculations. For the case of slow motion in the Cahn Hilliard equation this was pointed out by Elliott and French [22] Only recently has it been demonstrated that meaningful computation of slow motion is actually possible, compare for example Estep [23], Estep, Verduyn Lunel, and Williams [24] Estep and Williams [25] as well as Reyna and Ward [49] As the number of references attests, much analysis has been devoted to the study of slow motion of transition layers in the solutions to one dimensional bistable partial differential equations. ....
D. J. Estep. An analysis of numerical approximations of metastable solutions of the bistable equation. Nonlinearity, 7:1445--1462, 1994.
Global Dynamics of a Discontinuous Galerkin Approximation to.. - French, Jensen (1995) (Correct)
....approximation should resemble those of the true solution. In the study of nonlinear evolution problems long time behavior is often an important issue. Recently, many researchers have begun to investigate the long time behavior of discrete solutions (see for instance [B1] B2] E] EL] [ES], Es] EsS] FJ1] FJ2] HLR] HR] HeR] KL] S] It is usually crucial in these studies to show that the numerical method inherits certain energy properties from the partial differential equation. The discontinuous Galerkin method is a finite element technique to obtain arbitrary ....
....approximation should resemble those of the true solution. In the study of nonlinear evolution problems long time behavior is often an important issue. Recently, many researchers have begun to investigate the long time behavior of discrete solutions (see for instance [B1] B2] E] EL] ES] [Es], EsS] FJ1] FJ2] HLR] HR] HeR] KL] S] It is usually crucial in these studies to show that the numerical method inherits certain energy properties from the partial differential equation. The discontinuous Galerkin method is a finite element technique to obtain arbitrary order ....
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D. Estep, An analysis of numerical approximations of metastable solutions of the bistable equation, Nonlinearity 7:5 (1994), 1445-.
Slow Motion in Higher-Order Systems and.. - Kalies, VanderVorst, al. (1999) (Correct)
....concerning the reliability of such numerical calculations. For the case of slow motion in the CahnHilliard equation this was pointed out by Elliott and French [17] Only recently has it been demonstrated that meaningful computation of slow motion is actually possible, compare for example Estep [18], Estep, Verduyn Lunel, and Williams [19] Estep and Williams [20] as well as Reyna and Ward [39] As the number of references attests, much analysis has been devoted to the study of slow motion of transition layers in the solutions to one dimensional bistable partial differential equations. ....
D. J. Estep. An analysis of numerical approximations of metastable solutions of the bistable equation. Nonlinearity, 7:1445--1462, 1994.
Accounting for Stability: A Posteriori Error Estimates.. - Estep, Holst, Mikulencak (2001) Self-citation (Estep) (Correct)
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D. Estep, An analysis of numerical approximations of metastable solutions of the bistable equation, Nonlinearity, 7 (1994), pp. 1445--1462.
Accurate Parallel Integration of Large Sparse Systems of.. - Estep, Williams (1996) (2 citations) Self-citation (Estep) (Correct)
....computation is possible over the entire range of motion of a typical metastable solution. The standard a priori analysis, with an exponentially growing stability factor on the order of exp(C t=ffl 2 ) exp(1000t) for the ffl we use) rules this out quite definitely. It is possible to show[10] that accurate approximation is possible over the first metastable period, i.e. up to some time before the first transition when the wells have not collapsed too much, provided a certain threshold accuracy in space and time is maintained. This analysis does not indicate what happens during a ....
Estep, D., An analysis of numerical approximations of metastable solutions of the bistable equation, Nonlinearity 7 (1994), 1445--1662 .
Finite Element Center - Preprint Chalmers University (2004) (Correct)
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D. Estep, An analysis of numerical approximations of metastable solutions of the bistable equation, Nonlinearity, 7 (1994), pp. 1445--1462.
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