The Convection-Diffusion-Reaction Equation in Non-Hilbert Sobolev Spaces: A Direct Proof of the Inf-Sup Condition and Stability of Galerkin's Method

Paul Houston, Ignacio Muga, Sarah Roggendorf, Kristoffer G. Van Der Zee

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

5 Citas (Scopus)

Resumen

While it is classical to consider the solution of the convection-diffusion-reaction equation in the Hilbert space {equation presented}, the Banach Sobolev space{equation presented}, is more general allowing more irregular solutions. In this paper we present a well-posedness theory for the convection-diffusion-reaction equation in the {equation presented}. The theory is based on directly establishing the inf-sup conditions. Apart from a standard assumption on the advection and reaction coefficients, the other key assumption pertains to a subtle regularity requirement for the standard Laplacian. An elementary consequence of the well-posedness theory is the stability and convergence of Galerkin's method in this setting, for a diffusion-dominated case and under the assumption of {equation presented}-projector.

Idioma originalInglés
Páginas (desde-hasta)503-522
Número de páginas20
PublicaciónComputational Methods in Applied Mathematics
Volumen19
N.º3
DOI
EstadoPublicada - 1 jul 2019
Publicado de forma externa

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