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

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.
spectral method, adaptivity, convergence, optimal cardinality
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1002819
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