17th GAMM-Seminar Leipzig on
Construction of Grid Generation Algorithms

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
Phone: +49.341.9959.752, Fax: +49.341.9959.999

  17th GAMM-Seminar
February, 1st-3rd, 2001
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  Abstract Carsten Carstensen, Thu, 12.00-12.25 Previous Contents Next  
  Which Adaptive FE Spaces Allow for a H1-Stable L2-Projection?
Carsten Carstensen (Uni Kiel)

Within automatic mesh-refining algorithms, the focus is on good properties of the designed mesh such as regularity (no hanging nodes) and shape regularity (no degenerated angles or aspect ratios). This presentation is, in addition, concerned with a stability property of the generated finite element spaces.

The presentation briefly reports on a recent result on the uniform H1-stability of the L2-projection onto the discrete space. The affirmative result states that any red-green-blue-refinement generates conforming piecewise affine spaces on triangles where the bound for the L2-projection only depends on the coarse mesh. The underlying criterion on the commutator property of local mass matrices with certain weighted diagonal matrices is based on recent work of Bramble, Pasciak, and Steinbach. The diagonal matrices measure the refinement levels and the criterion limits the refinement which should not be too high - as expected from a criterion due to Crouzeix and Thomee.

Unfortunatly, the proof fails for parallelograms or three-dimensional situations. The presentation addresses those general situations and discusses extra conditions on the refinement procedure in order to keep the L2-projection onto the finite element spaces uniformly H1-stable.

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Last updated:
30.11.2004 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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