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

  • M. Aurada (a1), M. Feischl (a1), J. Kemetmüller (a1), M. Page (a1) and D. Praetorius (a1)...

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.

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Keywords

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

  • M. Aurada (a1), M. Feischl (a1), J. Kemetmüller (a1), M. Page (a1) and D. Praetorius (a1)...

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