High order compact finite difference methods for non-Fickian flows in porous media

High-Order Compact Finite Difference Methods

In this work we present a general approach for developing high-order compact differencing schemes by utilizing the governing differential equation to help approximate truncation error terms. As an illustrative application we consider the stream-function vorticity form of the Navier Stokes equations, and provide driven cavity results. Some extensions to treat non-constant metric coefficients res...

Sharp L-error Estimates and Superconvergence of Mixed Finite Element Methods for Non-fickian Flows in Porous Media∗

Abstract. A sharper L-error estimate is obtained for the non-Fickian flow of fluid in porous media by means of a mixed Ritz–Volterra projection instead of the mixed Ritz projection used in [R. E. Ewing, Y. Lin, and J. Wang, Acta Math. Univ. Comenian. (N.S.), 70 (2001), pp. 75–84]. Moreover, local L superconvergence for the velocity along the Gauss lines and for the pressure at the Gauss points ...

Sharp L2-Error Estimates and Superconvergence of Mixed Finite Element Methods for Non-Fickian Flows in Porous Media

Compact finite difference methods for high order integro-differential equations

High order integro-differential equations (IDE), especially nonlinear, are usually difficult to solve even for approximate solutions. In this paper, we give a high accurate compact finite difference method to efficiently solve integro-differential equations, including high order and nonlinear problems. By numerical experiments, we show that compact finite difference method of integro-differenti...

High Order Compact Finite Difference Schemes for Solving Bratu-Type Equations

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...