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.

We consider the solution of second order elliptic PDEs in Rd 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 H1 / 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 H1 / 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.

DOI : 10.1051/m2an/2013069
Classification : 65N30, 65N50
Mots-clés : 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},
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     url = {http://www.numdam.org/articles/10.1051/m2an/2013069/}
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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. http://www.numdam.org/articles/10.1051/m2an/2013069/

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