Optimal order a posteriori error estimates for a class of Runge-Kutta and Galerkin methods

Akrivis, George, Makridakis, Charalambos and Nochetto, Ricardo H (2009) Optimal order a posteriori error estimates for a class of Runge-Kutta and Galerkin methods. Numerische Mathematik, 114 (1). pp. 133-160. ISSN 0029-599X

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Abstract

We derive a posteriori error estimates, which exhibit optimal global order, for a class of time stepping methods of any order that include Runge–Kutta Collocation (RK-C) methods and the continuous Galerkin (cG) method for linear and nonlinear stiff ODEs and parabolic PDEs. The key ingredients in deriving these bounds are appropriate one-degree higher continuous reconstructions of the approximate solutions and pointwise error representations. The reconstructions are based on rather general orthogonality properties and lead to upper and lower bounds for the error regardless of the time-step; they do not hinge on asymptotics.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Richard Chambers
Date Deposited: 21 May 2013 09:43
Last Modified: 21 May 2013 09:43
URI: http://sro.sussex.ac.uk/id/eprint/44786
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