Article ID Journal Published Year Pages File Type
1703216 Applied Mathematical Modelling 2014 17 Pages PDF
Abstract

In this paper, the center finite difference (CFD) method for the elliptic equation is deduced by the P1P1-element and the first-order discrete partial differential equation over the dual element K∗K∗ in the 1D or 2D domain. Next, the coefficient matrix of the CFD method is explicitly reduced and the H1H1-stability and convergence of the CFD solution uhuh is provided. Furthermore, the H1H1-super-convergence of uhuh to IhuIhu is obtained under the case of the almost-uniform mesh. Based on the H1H1-super-convergence of uhuh to IhuIhu, the optimal L2L2-error estimate of the numerical solution uhuh and the H1H1-super-convergence error estimate of the interpolation solution I2h2uh are derived respectively. Finally, some numerical tests are made to show the analytical results of the CFD method.

Related Topics
Physical Sciences and Engineering Engineering Computational Mechanics
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