Journal article
On the Sharpness of L 2 -Error Estimates of H 1 0 -Projections Onto Subspaces of Piecewise High-Order Polynomials
Mathematics of computation, Vol.64(209), p.51
1995
DOI: 10.2307/2153322
Abstract
In a plane polygonal domain, consider a Poisson problem −Δu = f with homogeneous Dirichlet boundary condition and the p-version finite element solutions of this. We give various upper and lower bounds for the error measured in L 2 . In the case of a single element (i.e., a convex domain), we reduce the question of sharpness of these estimates to the behavior of a certain inf-sup constant, which is numerically determined, and a likely sharp estimate is then conjectured. This is confirmed during a series of numerical experiments also for the case of a reentrant comer. For a one-dimensional analogue problem (of rotational symmetry), sharp L 2 -error estimates are proven directly and via an extension of the classical duality argument. Here, we give sharp L∞-error estimates in some weighted and unweighted norms also
Details
- Title: Subtitle
- On the Sharpness of L 2 -Error Estimates of H 1 0 -Projections Onto Subspaces of Piecewise High-Order Polynomials
- Creators
- Weimin HanSoren Jensen
- Resource Type
- Journal article
- Publication Details
- Mathematics of computation, Vol.64(209), p.51
- DOI
- 10.2307/2153322
- ISSN
- 0025-5718
- eISSN
- 1088-6842
- Language
- English
- Date published
- 1995
- Academic Unit
- Mathematics
- Record Identifier
- 9983985960302771
Metrics
9 Record Views