Abstract
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.
Original language | English |
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Pages (from-to) | 503-522 |
Number of pages | 20 |
Journal | Computational Methods in Applied Mathematics |
Volume | 19 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jul 2019 |
Keywords
- Banach Spaces
- Convection-Diffusion Equation
- Elliptic Regularity
- FEM
- Galerkin Methods
- Inf-Sup Condition
- Well-Posedness