Finite Element Multigrid Method for the Boundary Value Problem of Fractional Advection Dispersion Equation
نویسندگان
چکیده
The stationary fractional advection dispersion equation is discretized by linear finite element scheme, and a full V-cycle multigrid method (FV-MGM) is proposed to solve the resulting system. Some useful properties of the approximation and smoothing operators are proved. Using these properties we derive the convergence results in both L2 norm and energy norm for FV-MGM. Numerical examples are given to demonstrate the convergence rate and efficiency of the method.
منابع مشابه
The new implicit finite difference method for the solution of time fractional advection-dispersion equation
In this paper, a numerical solution of time fractional advection-dispersion equations are presented.The new implicit nite dierence methods for solving these equations are studied. We examinepractical numerical methods to solve a class of initial-boundary value fractional partial dierentialequations with variable coecients on a nite domain. Stability, consistency, and (therefore) convergenceof t...
متن کاملTwo-dimensional advection-dispersion equation with depth- dependent variable source concentration
The present work solves two-dimensional Advection-Dispersion Equation (ADE) in a semi-infinite domain. A variable source concentration is regarded as the monotonic decreasing function at the source boundary (x=0). Depth-dependent variables are considered to incorporate real life situations in this modeling study, with zero flux condition assumed to occur at the exit boundary of the domain, i.e....
متن کاملA numerical scheme for space-time fractional advection-dispersion equation
In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...
متن کاملTwo-dimensional advection-dispersion equation with depth- dependent variable source concentration
The present work solves two-dimensional Advection-Dispersion Equation (ADE) in a semi-infinite domain. A variable source concentration is regarded as the monotonic decreasing function at the source boundary (x=0). Depth-dependent variables are considered to incorporate real life situations in this modeling study, with zero flux condition assumed to occur at the exit boundary of the domain, i.e....
متن کاملNumerical approximation of a one-dimensional space fractional advection-dispersion equation with boundary layer
Finite element computations for singularly perturbed convection-diffusion equations have long been an attractive theme for numerical analysis. In this article, we consider the singularly perturbed fractional advection-dispersion equation (FADE) with boundary layer behavior. We derive a theoretical estimate which shows that the under-resolved case corresponds to ǫ < hα−1, where α is the order of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Applied Mathematics
دوره 2013 شماره
صفحات -
تاریخ انتشار 2013