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Pointwise a posteriori error estimates for monotone semi-linear equations. (English) Zbl 1104.65107
A continuous barrier function $$w$$ is determined such that the solution of the continuous problem lies between $$u_h-w$$ and $$u_h+w$$. Negative norms of the residues are estimated and the continuous maximum principle is applied. The technique that has been used by R. H. Nochetto, K. G. Siebert and A. Veeser [ibid. 95, No. 1, 163–195 (2003; Zbl 1027.65089); SIAM J. Numer. Anal. 42, No. 5, 2118–2135 (2005; Zbl 1095.65099)] to linear problems, is extended here to monotone semi-linear equations. Numerical experiments illustrate reliability and efficiency properties of the corresponding estimators and investigate the performance of the resulting adaptive algorithms in terms of the polynomial order and quadrature.

##### MSC:
 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000) 35J65 Nonlinear boundary value problems for linear elliptic equations
##### Keywords:
numerical experiments; algorithms
ALBERTA; ALBERT
Full Text:
##### References:
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