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On the sharpness of L2-error estimates of H01-projections onto subspaces of piecewise, high-order polynomials
Journal article   Open access   Peer reviewed

On the sharpness of L2-error estimates of H01-projections onto subspaces of piecewise, high-order polynomials

WEIMIN Han and S Jensen
Mathematics of computation, Vol.64(209), pp.51-70
1995
DOI: 10.1090/S0025-5718-1995-1270620-X
url
https://doi.org/10.1090/S0025-5718-1995-1270620-XView
Published (Version of record) Open Access

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 L2. 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 corner. For a one-dimensional analogue problem (of rotational symmetry), sharp L2-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. © 1995 American Mathematical Society.
 Mathematics Numerical Analysis Exact sciences and technology Numerical analysis. Scientific computation Partial differential equations, boundary value problems Sciences and techniques of general use

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