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

08.08.2017

Superconvergence of Immersed Finite Volume Methods for One-Dimensional Interface Problems

verfasst von: Waixiang Cao, Xu Zhang, Zhimin Zhang, Qingsong Zou

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

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Abstract

In this paper, we introduce a class of high order immersed finite volume methods (IFVM) for one-dimensional interface problems. We show the optimal convergence of IFVM in \(H^1\)- and \(L^2\)-norms. We also prove some superconvergence results of IFVM. To be more precise, the IFVM solution is superconvergent of order \(p+2\) at the roots of generalized Lobatto polynomials, and the flux is superconvergent of order \(p+1\) at generalized Gauss points on each element including the interface element. Furthermore, for diffusion interface problems, the convergence rates for IFVM solution at the mesh points and the flux at generalized Gauss points can both be raised to 2p. These superconvergence results are consistent with those for the standard finite volume methods. Numerical examples are provided to confirm our theoretical analysis.
Vorheriger Artikel A High Order Conservative Semi-Lagrangian Discontinuous Galerkin Method for Two-Dimensional Transport Simulations
Nächster Artikel DG-IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

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Metadaten
Titel
Superconvergence of Immersed Finite Volume Methods for One-Dimensional Interface Problems
verfasst von
Waixiang Cao
Xu Zhang
Zhimin Zhang
Qingsong Zou
Publikationsdatum
08.08.2017
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/s10915-017-0532-6

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