Discontinuous finite volume element methods and its applications
| Speaker |
Colloquium by Sarvesh Kumar, Dept. of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram
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|---|---|
| When |
Oct 20, 2015
from 04:00 PM to 05:00 PM |
| Where | LH006 |
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Abstract
In this talk, first we would like to address the convergence issues of a standard finite volume element method (FVEM) applied to simple elliptic problems. Then, we discuss discontinuous finite volume element methods (DFVEM) for elliptic problems and its advantages over the standard FVEM. Further, we present a natural extension of DFVEM which was employed for elliptic problems, to the Stokes problems.
We also talk about the applications of DFVEM for the approximation of miscible displacement problems. The mathematical model which describe the miscible displacement of one incompressible fluid by another in a porous medium is modeled by two coupled nonlinear partial differential equations; one is pressure-velocity equation and other is concentration equation. In this talk, we discuss a mixed FVEM for the approximation of the pressure-velocity equation and a DFVEM for the concentration equation. Also, a priori error estimates for velocity, pressure and concentration will be shown. Some Numerical experiments will be presented to substantiate the validity of the theoretical results.