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.
Adaptive Spectral Galerkin Methods with Dynamic Marking
VERANI, MARCO
2016-01-01
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.File in questo prodotto:
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