Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes

Schieweck, Friedhelm

doi:10.1051/m2an:2008014

Schieweck, Friedhelm

ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 3, pp. 493-505

Résumé

We consider a family of quadrilateral or hexahedral mixed $h p$ -finite elements for an incompressible flow problem with $Q_{r}$ -elements for the velocity and discontinuous $P_{r - 1}$ -elements for the pressure where the order $r$ can vary from element to element between $2$ and an arbitrary bound. For multilevel adaptive grids with hanging nodes and a sufficiently small mesh size, we prove the inf-sup condition uniformly with respect to the mesh size and the polynomial degree.

MR Zbl

DOI : 10.1051/m2an:2008014

Classification : 65N30, 65N35, 76D07
Keywords: Stokes problem, inf-sup condition, mixed $hp$-FEM, quadrilateral and hexahedral finite elements, multilevel adaptive grids, hanging nodes

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     title = {Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {493--505},
     year = {2008},
     publisher = {EDP Sciences},
     volume = {42},
     number = {3},
     doi = {10.1051/m2an:2008014},
     mrnumber = {2423796},
     zbl = {1154.76034},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/m2an:2008014/}
}

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Schieweck, Friedhelm. Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes. ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 3, pp. 493-505. doi: 10.1051/m2an:2008014

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