Publications in Scientific Journals:
M. Aurada, M. Feischl, J. Kemetmüller, M. Page, D. Praetorius:
"Each H1/2-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in Rd";
M2AN Math. Model. Numer. Anal.,
47
(2013),
04;
1207
- 1235.
English abstract:
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 $p\in\N$. As model example serves the Poisson equation with mixed Dirichlet-Neumann boundary conditions, where the inhomogeneous Dirichlet data are discretized by use of a stable projection, for instance, the $L^2$-projection for $p=1$ or the Scott-Zhang projection for general $p\ge1$. For error estimation, we use a residual error estimator which includes the Dirichlet data oscillations. We prove convergence of the adaptive algorithm even with quasi-optimal convergence rate. Numerical experiments conclude the work.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1051/m2an/2013069
Created from the Publication Database of the Vienna University of Technology.