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Journal of Scientific Computing

Erschienen in:

26.04.2017

Optimally Convergent HDG Method for Third-Order Korteweg–de Vries Type Equations

verfasst von: Bo Dong

Erschienen in: Journal of Scientific Computing | Ausgabe 2-3/2017

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Abstract

We develop and analyze a new hybridizable discontinuous Galerkin method for solving third-order Korteweg–de Vries type equations. The approximate solutions are defined by a discrete version of a characterization of the exact solution in terms of the solutions to local problems on each element which are patched together through transmission conditions on element interfaces. We prove that the semi-discrete scheme is stable with proper choices of stabilization function in the numerical traces. For the linearized equation, we carry out error analysis and show that the approximations to the exact solution and its derivatives have optimal convergence rates. In numerical experiments, we use an implicit scheme for time discretization and the Newton–Raphson method for solving systems of nonlinear equations, and observe optimal convergence rates for both the linear and the nonlinear third-order equations.

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Titel: Optimally Convergent HDG Method for Third-Order Korteweg–de Vries Type Equations
verfasst von: Bo Dong
Publikationsdatum: 26.04.2017
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2-3/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0437-4

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