Abstract
In this paper, we construct a semi-discrete scheme and a fully discrete scheme using the Wilson nonconforming element for the parabolic integro-differential equation arising in modeling the non-Fickian flow in porous media by the interior penalty method. Without using the conventional elliptic projection, which was an indispensable tool in the convergence analysis of finite element methods in previous literature, we get an optimal error estimate which is only determined by the interpolation error. Finally, we give some numerical experiments to show the efficiency of the method.
Highlights
1 Introduction Consider the numerical solution of the non-Fickian flow in porous media modeled by an initial boundary value problem of the following parabolic integro-differential equation:
Without using the conventional elliptic projection, which was an indispensable tool in the convergence analysis of finite element methods in previous literature, we get an optimal error estimate which is only determined by the interpolation error
We get an optimal error estimate which is only determined by the interpolation error
Summary
Consider the numerical solution of the non-Fickian flow in porous media modeled by an initial boundary value problem of the following parabolic integro-differential equation:. Provided a framework for the analysis of a large class of discontinuous methods for secondorder elliptic problems in [ ] and a semi-discrete finite element procedure for the secondorder parabolic initial boundary value problem in [ ]. For a fourth-order elliptic boundary value problem, Engel et al [ ] proposed an interior penalty method that uses only the standard C finite elements. Without using the conventional elliptic projection, which was an indispensable tool in the convergence analysis of finite element methods in previous literature, we get an optimal error estimate which is only determined by the interpolation error.
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