标题：A block-centered finite difference method for the nonlinear Sobolev equation on nonuniform rectangular grids
作者：Li, Xiaoli ;Rui, Hongxing
作者机构：[Li, Xiaoli ] School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, 更多
来源：Applied Mathematics and Computation
关键词：Block-centered finite difference; Nonlinear Sobolev equation; Nonuniform rectangular grids; Numerical experiments; Stability
摘要：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. © 2019 Elsevier Inc.