Publication

Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems

2004
Journal Articles

Abstract

In this paper we recall a stabilization technique for finite element methods for convection-diffusion-reaction equations, originally proposed by Douglas and Dupont. The method uses least square stabilization of the gradient jumps a across element boundaries. We prove that the method is stable in the hyperbolic limit and prove optimal a priori error estimates. We address the question of monotonicity of discrete solutions and present some numerical examples illustrating the theoretical results

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2004
Journal Articles

Abstract

Official source

Related concepts (30)

Diffusion

Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, like in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios.

Finite element method

The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).

Reaction–diffusion system

Reaction–diffusion systems are mathematical models which correspond to several physical phenomena. The most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space. Reaction–diffusion systems are naturally applied in chemistry. However, the system can also describe dynamical processes of non-chemical nature.

Related publications (24)

Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems

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Mimetic finite difference schemes for transport operators with divergence-free advective field and applications to plasma physics

Accompanying dataset for the paper: "Adaptive FEM-DEM bridging coupling to study third-body evolution in sheared granular media"

Contributions

Funding sources

Data structure and information

ETLA-3D: Equivalent Thin Layer Aggregation based Thermal FEM for Hybrid Bonding F2F 3D ICs