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- Joseé Manuel Cascon, Christian Kreuzer, Ricardo H. Nochetto, Kunibert G. Siebert
- SIAM J. Numerical Analysis
- 2008

We analyze the simplest and most standard adaptive finite element method (AFEM), with any polynomial degree, for general second order linear, symmetric elliptic operators. As is customary in practice, the AFEM marks exclusively according to the error estimator and performs a minimal element refinement without the interior node property. We prove that the… (More)

We examine adaptive finite element methods (AFEM) with any polynomial degree satisfying rather general assumptions on the a posteriori error estimators. We show that several non-residual estimators satisfy these assumptions. We design an AFEM with single Dörfler marking for the sum of error estimator and oscillation, prove a contraction property for the… (More)

We design an adaptive finite element method (AFEM) for mixed boundary value problems associated with the differential operator A − ∇div in H(div,Ω). For A being a variable coefficient matrix with possible jump discontinuities, we provide a complete a posteriori error analysis which applies to both Raviart–Thomas RT and Brezzi– Douglas–Marini BDM elements of… (More)

- Andrea Bonito, Joseé Manuel Cascon, Khamron Mekchay, Pedro Morin, Ricardo H. Nochetto
- Foundations of Computational Mathematics
- 2016

We present a new AFEM for the Laplace-Beltrami operator with arbitrary polynomial degree on parametric surfaces, which are globally W 1 ∞ and piecewise in a suitable Besov class embedded in C1,α with α ∈ (0, 1]. The idea is to have the surface sufficiently well resolved in W 1 ∞ relative to the current resolution of the PDE in H1. This gives rise to a… (More)

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