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Bernardo Cockburn (2003)
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Differential Equations, Vol. 41, No. 7, 2005, pp. 970–983. Translated from Differentsial'nye Uravneniya, Vol. 41, No. 7, 2005, pp. 925–937. Original Russian Text Copyright c 2005 by Gaevskaya, Repin. NUMERICAL METHODS A Posteriori Error Estimates for Approximate Solutions of Linear Parabolic Problems A. V. Gaevskaya and S. I. Repin St. Petersburg State Polytechnic University, St. Petersburg, Russia St. Petersburg Division of the Steklov Mathematical Institute, Russian Academy of Sciences, St. Petersburg, Russia Received March 1, 2005 1. INTRODUCTION Nowadays, there are several well-known numerical methods for solving initial-boundary value problems for parabolic equations, which, in particular, include nite-di erence methods, the - nite element methods (e.g., see [1{3]), and the discontinuous Galerkin method, widely used in the recent years (e.g., see [4]). In addition to the stability and consistency of the corresponding schemes, the accuracy of the approximate solution is also important in the analysis of these meth- ods. As a rule, the analysis of accuracy was earlier performed in the framework of the so-called apriori (asymptotic) approach, which uses apriori information on the regularity of the exact so- lution and properties of the approximations and permits one to estimate the asymptotic order of decay of the error. A
Differential Equations – Springer Journals
Published: Sep 30, 2005
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