M. Karkulik, D. Pavlicek, D. Praetorius:

"On 2D newest vertex bisection: Optimality of mesh-closure and H^1-stability of L_2-projection";

in: "ASC Report 10/2012", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2012, ISBN: 978-3-902627-05-6, 1 - 28.

Newest vertex bisection (NVB) is a popular local mesh-refinement

strategy for regular triangulations which consist of simplices. For

the 2D case, we prove that the meshclosure step of NVB, which

preserves regularity of the triangulation, is quasi-optimal and that

the corresponding L2-projection onto lowest-order Courant finite

elements (P1-FEM) is always H1-stable. Throughout, no additional

assumptions on the initial triangulation are imposed. Our analysis

thus improves results of Binev, Dahmen & DeVore (Numer. Math. 97,

2004), Carstensen (Constr. Approx. 20, 2004), and Stevenson (Math.

Comp. 77, 2008) in the sense that all assumptions of their theorems

are removed. Consequently, our results relax the requirements under

which adaptive finite element schemes can be mathematically

guaranteed to convergence with quasi-optimal rates.

adaptive finite element methods, regular triangulations, newest vertex bisection, L^2-projection, H^1-stability

http://www.asc.tuwien.ac.at/preprint/2012/asc10x2012.pdf

Created from the Publication Database of the Vienna University of Technology.