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.
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