A GALERKIN FINITE ELEMENT METHOD TO SOLVE FRACTIONAL DIFFUSION AND FRACTIONAL DIFFUSION-WAVE EQUATIONS
نویسندگان
چکیده
منابع مشابه
A Petrov-Galerkin Finite Element Method for Fractional Convection-Diffusion Equations
In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo derivative of order α ∈ (3/2, 2) in the leading term and both convection and potential terms. They arise in the mathematical modeling of asymmetric super-diffusion processes in heterogeneous media. The well-posedness of t...
متن کاملDiscontinuous Galerkin Methods for Fractional Diffusion Equations
We consider the development and analysis of local discontinuous Galerkin methods for fractional diffusion problems, characterized by having fractional derivatives, parameterized by β ∈ [1, 2]. We show through analysis that one can construct a numerical flux which results in a scheme that exhibit optimal order of convergence O(hk+1) in the continuous range between pure advection (β = 1) and pure...
متن کاملDiscontinuous Galerkin Method for Fractional Convection-Diffusion Equations
We propose a discontinuous Galerkin method for fractional convection-diffusion equations with a superdiffusion operator of order α(1 < α < 2) defined through the fractional Laplacian. The fractional operator of order α is expressed as a composite of first order derivatives and a fractional integral of order 2 − α. The fractional convection-diffusion problem is expressed as a system of low order...
متن کاملThe discontinuous Galerkin method for fractional degenerate convection-diffusion equations
We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (Lévy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through n...
متن کاملSuperconvergence of a Discontinuous Galerkin Method for Fractional Diffusion and Wave Equations
We consider an initial-boundary value problem for ∂tu−∂ t ∇2u = f(t), that is, for a fractional diffusion (−1 < α < 0) or wave (0 < α < 1) equation. A numerical solution is found by applying a piecewise-linear, discontinuous Galerkin (DG) method in time combined with a piecewiselinear, conforming finite element method in space. The time mesh is graded appropriately near t = 0, but the spatial m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Modelling and Analysis
سال: 2013
ISSN: 1392-6292,1648-3510
DOI: 10.3846/13926292.2013.783884