Convergence rates for an adaptive dual weighted residual finite element algorithm. (English) Zbl 1101.65103

Error estimates for functionals are considered, i.e. \(\langle F, u-u_n\rangle\) with \(F\) being a functional and \(u_n\) a finite element approximation of \(u\) in \(d\)-space. Error representations of the form \[ \text{error}=\sum_{\text{elements}} \text{error density}\times h^{2+d}_{\text{element}} \] are derived. The representation show in which part of the domain refinements bring the best profit, and how the error indicators become approximately equidistributed. Moreover, convergence and a geometrical decay of the error is a consequence.


65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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