Parabolic Approximations of the Convection - Diffusion Equation
نویسنده
چکیده
We propose an approximation of the convection-diffusion operator which consists in the product of two parabolic operators. This approximation is much easier to solve than the full convection-diffusion equation, which is elliptic in space. We prove that this approximation is of order three in the viscosity and that the classical parabolic approximation is of order one in the viscosity. Numerical examples are given to demonstrate the effectiveness of our new approximation.
منابع مشابه
Reduced Basis Method for Finite Volume Approximation of Evolution Equations on Parametrized Geometries
In this paper we discuss parametrized partial differential equations (PDEs) for parameters that describe the geometry of the underlying problem. One can think of applications in control theory and optimization which depend on time-consuming parameter-studies of such problems. Therefore, we want to reduce the order of complexity of the numerical simulations for such PDEs. Reduced Basis (RB) meth...
متن کاملAsymptotics of Blowup for a Convection-diffusion Equation with Conservation
This paper deals with a parabolic partial differential equation that incorporates diffusion and convection terms and that previously has been shown to have solutions that become unbounded at a single point in finite time. The results presented here describe the limiting behavior of the solution in a neighborhood of the blowup point, as well as the asymptotic growth rate as the blowup time is ap...
متن کاملThe conservation law is a parabolic reaction-convection-diffusion equation with a small parameter multiplying the diffusion term and convex flux. Rigorous upper and lower bounding functions for the solution of the conservation law
The size of the shock-layer governed by a conservation law is studied. The conservation law is a parabolic reaction-convection-diffusion equation with a small parameter multiplying the diffusion term and convex flux. Rigorous upper and lower bounding functions for the solution of the conservation law are established based on maximum-principle arguments. The bounding functions demonstrate that t...
متن کاملApplication Of Alternating Group Explicit Method For Parabolic Equations
Qinghua Feng School of Science Shandong university of technology Zhangzhou Road 12#, Zibo , Shandong, 255049 China [email protected] Abstract: Based on the concept of decomposition, two alternating group explicit methods are constructed for 1D convection-diffusion equation with variable coefficient and 2D diffusion equations respectively. Both the two methods have the property of unconditional sta...
متن کاملFinite Element Methods for Convection Diffusion Equation
This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...
متن کامل