Work

Adaptive Spectral Galerkin Methods with Dynamic Marking

Year: 2016

Type: article

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.

Source: SIAM Journal on Numerical Analysis

DOI: 10.1137/15m104579x

Authors: Claudio Canuto, Ricardo H. Nochetto, Rob Stevenson, Marco Verani

Institutions: Politecnico di Torino, University of Maryland, College Park, University of Amsterdam, Politecnico di Milano

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per il Calcolo Scientifico, Division of Mathematical Sciences

Awards: Adaptive Finite Element Methods for Multiscale Geometric PDE: Modeling, Analysis, and Computation, Nonlinear Multiscale Phenomena: Analysis, Control, and Computation, G5698880408, G8195706232