Preprint

Adaptive Spectral Galerkin Methods with Dynamic Marking

Claudio CanutoPolytechnic University of TurinRicardo H. NochettoUniversity of Maryland - College ParkRob StevensonUniversity of AmsterdamMarco VeraniPolytechnic University of Milan

SIAM Journal on Numerical Analysisjournal2016en

ABI

Abstract

The convergence and optimality theory of adaptive Galerkin methods is almost exclusively based on the Dörfler marking. This entails a fixed parameter and leads to a contraction constant bounded below away from zero. For spectral Galerkin methods this is a severe limitation which affects performance. We present a dynamic marking strategy that allows for a superlinear relation between consecutive discretization errors, and show exponential convergence with linear computational complexity whenever the solution belongs to a Gevrey approximation class.

Topics

Advanced Numerical Methods in Computational Mathematics Numerical methods for differential equations Model Reduction and Neural Networks

Identifiers

DOI: 10.1137/15m104579x

Citations and references

Cited by 018 references

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