An exponential fitting scheme for general convection-diffusion equations on tetrahedral meshes

Abstract

This paper contains construction and analysis a finite element approximation for convection dominated diffusion problems with full coefficient matrix on general simplicial partitions in $R^d$, $d=2,3$. This construction is quite close to the scheme of Xu and Zikatanov (Math. Comp. 1999) where a diagonal coefficient matrix has been considered. The scheme is of the class of exponentially fitted methods that does not use upwind or checking the flow direction. It is stable for sufficiently small discretization step-size assuming that the boundary value problem for the convection-diffusion equation is uniquely solvable. Further, it is shown that, under certain conditions on the mesh the scheme is monotone. Convergence of first order is derived under minimal smoothness of the solution.

12 pages, no figures; (Obchysljuval'na ta prykladna matematyka, Kiev)

Cited by in corpus (7)

• Steady-state Simulation of Semiconductor Devices using Discontinuous Galerkin Methods
• Multiscale Modeling and Simulation of Organic Solar Cells
• Analytical and Numerical Study of Photocurrent Transients in Organic Polymer Solar Cells
• A robust hybridizable discontinuous Galerkin scheme with harmonic averaging technique for steady state of real-world semiconductor devices
• Low Regularity Primal-Dual Weak Galerkin Finite Element Methods for Convection-Diffusion Equations
• Hierarchical Electrochemical Modeling and Simulation of Bio-Hybrid Interfaces
• Simplex-averaged finite element methods for $H(\mathrm{grad})$, $H(\mathrm{curl})$ and $H(\mathrm{div})$ convection-diffusion problems