Abstract
We study approximation properties of hp-finite element subspaces of $\boldsymbol{\mathsf{H}}(\mathop{{\rm div}},\Omega)$ and $\boldsymbol{\mathsf{H}}(\mathop{{\rm rot}},\Omega)$ on a polygonal domain $\Omega$ using Brezzi--Douglas--Fortin--Marini (BDFM) or Raviart--Thomas (RT) elements. Approximation theoretic results are derived for the hp-version finite element method on non-quasi-uniform meshes of quadrilateral elements with hanging nodes for functions belonging to weighted Sobolev spaces ${\boldsymbol{\mathsf{H}}}_{\omega}^{s,\ell}(\Omega)$ and the countably normed spaces $\pmb{{\cal B}}_{w}^{\ell}(\Omega)$. These results culminate in a proof of the characteristic exponential convergence property of the hp-version finite element method on suitably designed meshes under similar conditions needed for the analysis of the ${\boldsymbol{\mathsf{H}}}^{1}(\Omega)$ case. By way of illustration, exponential convergence rates are deduced for mixed hp-approximation of flow in porous media.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
