Isogeometric Residual Minimization Method (iGRM) with direction splitting preconditioner for stationary advection-dominated diffusion problems

Preconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation

Introduction Fractional differential equations (FDEs)  have  attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme  may be a good approach, particularly, the schemes in numerical linear algebra for solving ...

Global and Local Error Analysis for the Residual-Free Bubbles Method Applied to Advection-Dominated Problems

We prove the stability and a priori global and local error analysis for the residual-free bubbles finite element method applied to advection dominated advection-diffusion problems.

A robust a posteriori estimator for the Residual-free Bubbles method applied to advection-diffusion problems

A Simplified Solution for Advection Dominated Accretion Flows with Outflow

The existence of outflow in the advection dominated accretion flows has been confirmed by both numerical simulations and observations. The outow models for ADAF have been investigated by several groups with a simple self similar solution. But this solution is inaccurate at the inner regions and can not explain the emitted spectrum of the flow; so, it is necessary to obtain a global solution for...

An overlapping domain decomposition preconditioner for a class of discontinuous Galerkin approximations of advection-diffusion problems

We consider a scalar advection{di usion problem and a recently proposed discontinuous Galerkin approximation, which employs discontinuous nite element spaces and suitable bilinear forms containing interface terms that ensure consistency. For the corresponding sparse, nonsymmetric linear system, we propose and study an additive, two{level overlapping Schwarz preconditioner, consisting of a coars...