Quasi-optimal convergence rate of an AFEM for quasi-linear problems

Details Quasi-optimal convergence rate of an AFEM for quasi-linear problems Quasi-optimal convergence rate of an AFEM for quasi-linear problems

2010-10-06

arxiv.org/abs/1010.1251v1

Mathematics

Numerical Analysis

Scientific paper

We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for nonlinear elliptic second-order equations of monotone type. The adaptive algorithm is based on residual-type a posteriori error estimators and D\"orfler's strategy is assumed for marking. We first prove a contraction property for a suitable definition of total error, which is equivalent to the total error as defined by Casc\'on et al. (in SIAM J. Numer. Anal. 46 (2008), 2524--2550), and implies linear convergence of the algorithm. Secondly, we use this contraction to derive the optimal cardinality of the AFEM.

Affiliated with

Also associated with

No associations

Rating

Quasi-optimal convergence rate of an AFEM for quasi-linear problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quasi-optimal convergence rate of an AFEM for quasi-linear problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quasi-optimal convergence rate of an AFEM for quasi-linear problems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-429144