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

Houston, Paul; Muga, Ignacio; Roggendorf, Sarah; van der Zee, Kristoffer

doi:10.1515/cmam-2018-0198

Research Repository

All Outputs (2)

Two?Grid hp ?DGFEMs on Agglomerated Coarse Meshes (2019)
Journal Article

We generalise the a priori error analysis of two?grid hp?version discontinuous Galerkin finite element methods for strongly monotone second?order quasilinear elliptic partial differential equations to the case when coarse meshes consisting of general... Read More about Two?Grid hp ?DGFEMs on Agglomerated Coarse Meshes.

The Convection-Diffusion-Reaction Equation in Non-Hilbert Sobolev Spaces: A Direct Proof of the Inf-Sup Condition and Stability of Galerkin’s Method (2019)
Journal Article

While it is classical to consider the solution of the convection-diffusion-reaction equation in the Hilbert space H10(Ω), the Banach Sobolev space W1,q0(Ω), 1 less than ∞ , is more general allowing more irregular solutions. In this paper we present a... Read More about The Convection-Diffusion-Reaction Equation in Non-Hilbert Sobolev Spaces: A Direct Proof of the Inf-Sup Condition and Stability of Galerkin’s Method.