Picture of two heads

Open Access research that challenges the mind...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including those from the School of Psychological Sciences & Health - but also papers by researchers based within the Faculties of Science, Engineering, Humanities & Social Sciences, and from the Strathclyde Business School.

Discover more...

hp-Approximation theory for BDFM/RT finite elements and applications

Ainsworth, M. and Pinchedez, K. (2003) hp-Approximation theory for BDFM/RT finite elements and applications. SIAM Journal on Numerical Analysis, 40 (6). pp. 2047-2068. ISSN 0036-1429

Full text not available in this repository. (Request a copy from the Strathclyde author)

Abstract

We study approximation properties of hp-finite element subspaces of $oldsymbol{mathsf{H}}(mathop{{ m div}},Omega)$ and $oldsymbol{mathsf{H}}(mathop{{ m rot}},Omega)$ 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 ${oldsymbol{mathsf{H}}}_{omega}^{s,ell}(Omega)$ 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 ${oldsymbol{mathsf{H}}}^{1}(Omega)$ case. By way of illustration, exponential convergence rates are deduced for mixed hp-approximation of flow in porous media.