Each $H^{1/2}$-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in $R^d$

Aurada, M.; Feischl, M.; Kemetmüller, J.; Page, M.; Praetorius, D.

doi:10.1051/m2an/2013069

Geodesic

Parcourir par

Each

H^{1 / 2}

-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in

R^{d}

Aurada, M. ; Feischl, M. ; Kemetmüller, J. ; Page, M. ; Praetorius, D.

ESAIM: Mathematical Modelling and Numerical Analysis , Direct and inverse modeling of the cardiovascular and respiratory systems. Numéro spécial, Tome 47 (2013) no. 4, pp. 1207-1235

Voir la notice de l'article provenant de la source Numdam

Résumé

We consider the solution of second order elliptic PDEs in R^d with inhomogeneous Dirichlet data by means of an h-adaptive FEM with fixed polynomial order p ∈ N. As model example serves the Poisson equation with mixed Dirichlet-Neumann boundary conditions, where the inhomogeneous Dirichlet data are discretized by use of an H^1 / 2-stable projection, for instance, the L²-projection for p = 1 or the Scott-Zhang projection for general p ≥ 1. For error estimation, we use a residual error estimator which includes the Dirichlet data oscillations. We prove that each H^1 / 2-stable projection yields convergence of the adaptive algorithm even with quasi-optimal convergence rate. Numerical experiments with the Scott-Zhang projection conclude the work.

Zbl

DOI : 10.1051/m2an/2013069

Classification : 65N30, 65N50
Keywords: adaptive finite element method, convergence analysis, quasi-optimality, inhomogeneous Dirichlet data

@article{M2AN_2013__47_4_1207_0,
     author = {Aurada, M. and Feischl, M. and Kemetm\"uller, J. and Page, M. and Praetorius, D.},
     title = {Each $H^{1/2}$-stable projection yields convergence and quasi-optimality of adaptive {FEM} with inhomogeneous {Dirichlet} data in $R^d$},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1207--1235},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {4},
     year = {2013},
     doi = {10.1051/m2an/2013069},
     zbl = {1275.65078},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013069/}
}

TY  - JOUR
AU  - Aurada, M.
AU  - Feischl, M.
AU  - Kemetmüller, J.
AU  - Page, M.
AU  - Praetorius, D.
TI  - Each $H^{1/2}$-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in $R^d$
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2013
SP  - 1207
EP  - 1235
VL  - 47
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013069/
DO  - 10.1051/m2an/2013069
LA  - en
ID  - M2AN_2013__47_4_1207_0
ER  -

%0 Journal Article
%A Aurada, M.
%A Feischl, M.
%A Kemetmüller, J.
%A Page, M.
%A Praetorius, D.
%T Each $H^{1/2}$-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in $R^d$
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2013
%P 1207-1235
%V 47
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013069/
%R 10.1051/m2an/2013069
%G en
%F M2AN_2013__47_4_1207_0

Aurada, M.; Feischl, M.; Kemetmüller, J.; Page, M.; Praetorius, D. Each $H^{1/2}$-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in $R^d$. ESAIM: Mathematical Modelling and Numerical Analysis , Direct and inverse modeling of the cardiovascular and respiratory systems. Numéro spécial, Tome 47 (2013) no. 4, pp. 1207-1235. doi: 10.1051/m2an/2013069

Cité par Sources :