Publication

Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations

Erik Burman
2007
Journal Articles

Abstract

A continuous interior penalty hp-finite element method that penalizes the jump of the discrete solution across mesh interfaces is introduced. Error estimates are obtained for first-order and advection-dominated transport operators. The analysis relies on three technical results that are of independent interest: an hp- inverse trace inequality, a local discontinuous to continuous hp-interpolation result, and hp-error estimates for continuous L2-orthogonal projections.

Official source

https://infoscience.epfl.ch/entities/publication/d50d9597-eb0a-4656-b3c5-a68b1819c5ef

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Erik Burman
2007
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/d50d9597-eb0a-4656-b3c5-a68b1819c5ef

About this result

Related concepts (18)

Convection–diffusion equation

The convection–diffusion equation is a combination of the diffusion and convection (advection) equations, and describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. Depending on context, the same equation can be called the advection–diffusion equation, drift–diffusion equation, or (generic) scalar transport equation.

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.

Advection

In the field of physics, engineering, and earth sciences, advection is the transport of a substance or quantity by bulk motion of a fluid. The properties of that substance are carried with it. Generally the majority of the advected substance is also a fluid. The properties that are carried with the advected substance are conserved properties such as energy. An example of advection is the transport of pollutants or silt in a river by bulk water flow downstream. Another commonly advected quantity is energy or enthalpy.

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