Related papers: Galerkin Method for the numerical solution of the …
In this paper, the exponential B-spline functions are used for the numerical solution of the RLW equation. Three numerical examples related to propagation of single solitary wave, interaction of two solitary waves and wave generation are…
In this paper, the exponential B-spline Galerkin \ method is set up for getting the numerical solution of the Burgers' equation. Two numerical examples\ related to shock wave propogation and travelling wave are studied to illustrate the…
The functional distributions of particle trajectories have wide applications, including the occupation time in half-space, the first passage time, and the maximal displacement, etc. The models discussed in this paper are for characterizing…
We use a concept of weak asymptotic solution for homogeneous as well as non-homogeneous fractional advection dispersion type equations. Using Legendre scaling functions as basis, a numerical method based on Galerkin approximation is…
The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The…
This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using…
In this paper we investigate the numerical approximation of the fractional diffusion, advection, reaction equation on a bounded interval. Recently the explicit form of the solution to this equation was obtained. Using the explicit form of…
The following work presents a generalized (extended) finite element formulation for the advection-diffusion equation. Using enrichment functions that represent the exponential nature of the exact solution, smooth numerical solutions are…
We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (L\'evy) operator. We prove various stability estimates along with convergence results toward…
We analyze a Discontinuous Galerkin method for a problem with linear advection-reaction and $p$-type diffusion, with Sobolev indices $p\in (1, \infty)$. The discretization of the diffusion term is based on the full gradient including jump…
We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-square method is employed to ensure stability of the discrete…
In this paper, we present optimal error estimates of the local discontinuous Galerkin method with generalized numerical fluxes for one-dimensional nonlinear convection-diffusion systems. The upwind-biased flux with adjustable numerical…
We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of…
This paper focuses on the adaptive discontinuous Galerkin (DG) methods for the tempered fractional (convection) diffusion equations. The DG schemes with interior penalty for the diffusion term and numerical flux for the convection term are…
In convection-dominated flows, robustness of the spatial discretisation is a key property. While Interior Penalty Galerkin (IPG) methods already proved efficient in the situation of large mesh Peclet numbers, Arbitrary Lagrangian-Eulerian…
In this paper, we present an embedded staggered discontinuous Galerkin method for the convection-diffusion equation. The new method combines the advantages of staggered discontinuous Galerkin (SDG) and embedded discontinuous Galerkin (EDG)…
In this paper, a new variational formulation based on discontinuous Galerkin technique for a reaction-diffusion problem is introduced, and the discontinuous Galerkin technique of this work is different from the general discontinuous…
A hybridized discontinuous Galerkin method is proposed for solving 2D fractional convection-diffusion equations containing derivatives of fractional order in space on a finite domain. The Riemann-Liouville derivative is used for the spatial…
We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite…
We propose an discontinuous Galerkin local orthogonal decomposition multiscale method for convection-diffusion problems with rough, heterogeneous, and highly varying coefficients. The properties of the multiscale method and the…