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.
Original language | English |
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Pages (from-to) | 2047-2068 |
Number of pages | 21 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 40 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2003 |
Keywords
- finite elements
- corner singularities
- exponential convergence
- numerical analysis