A block-centered finite difference method for the nonlinear Sobolev equation on nonuniform rectangular grids

Xiaoli Li and Hongxing Rui

Applied Mathematics and Computation, 2019, vol. 363, issue C, -

Abstract: In this article, a block-centered finite difference method for the nonlinear Sobolev equation is introduced and analyzed. The stability and the global convergence of the scheme are proved rigorously. Some a priori estimates of discrete norms with superconvergence O(Δt+h2+k2) for scalar unknown p, its gradient u and its flux q are established on nonuniform rectangular grids, where Δt, h and k are the step sizes in time, space in x- and y-direction. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

Keywords: Block-centered finite difference; Nonlinear Sobolev equation; Stability; Nonuniform rectangular grids; Numerical experiments (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:363:y:2019:i:c:30

DOI: 10.1016/j.amc.2019.124607

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