# Each H1/2–stable projection yields convergence and quasi–optimality of adaptive FEM with inhomogeneous Dirichlet data in Rd

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

- Volume: 47, Issue: 4, page 1207-1235
- ISSN: 0764-583X

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topAurada, M., et al. "Each H1/2–stable projection yields convergence and quasi–optimality of adaptive FEM with inhomogeneous Dirichlet data in Rd." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.4 (2013): 1207-1235. <http://eudml.org/doc/273190>.

@article{Aurada2013,

abstract = {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.},

author = {Aurada, M., Feischl, M., Kemetmüller, J., Page, M., Praetorius, D.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {adaptive finite element method; convergence analysis; quasi–optimality; inhomogeneous Dirichlet data; convergence; quasi-optimality; stability; second-order elliptic equations; Poisson equation; mixed Dirichlet-Neumann boundary conditions; Scott-Zhang projection; error estimation; numerical experiments},

language = {eng},

number = {4},

pages = {1207-1235},

publisher = {EDP-Sciences},

title = {Each H1/2–stable projection yields convergence and quasi–optimality of adaptive FEM with inhomogeneous Dirichlet data in Rd},

url = {http://eudml.org/doc/273190},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Aurada, M.

AU - Feischl, M.

AU - Kemetmüller, J.

AU - Page, M.

AU - Praetorius, D.

TI - Each H1/2–stable projection yields convergence and quasi–optimality of adaptive FEM with inhomogeneous Dirichlet data in Rd

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 4

SP - 1207

EP - 1235

AB - 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.

LA - eng

KW - adaptive finite element method; convergence analysis; quasi–optimality; inhomogeneous Dirichlet data; convergence; quasi-optimality; stability; second-order elliptic equations; Poisson equation; mixed Dirichlet-Neumann boundary conditions; Scott-Zhang projection; error estimation; numerical experiments

UR - http://eudml.org/doc/273190

ER -

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