Constants in Clément-interpolation error and residual based a posteriori error estimates in finite element methods. (English) Zbl 0973.65091

Residual based adaptive finite element methods applied to Laplace equations involve constants:
– in front of a weighted volume term;
– in front of weighted stress jumps across inner-element boundaries.
The aim of this paper is to establish explicit formulae for these constants by using the shape of the elements only. This leads to a straightforward hard-analysis, the results of which are compared with some numerical experiments reported in the final section of the work.
In some way, this paper puts the final piece to a class of a fully reliable a posteriori finite element error analysis.


65N15 Error bounds for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs