A posteriori error estimates of the discontinuous Galerkin method for the heat conduction equation
Ivana Šebestová, V. Dolejší (2012)
Acta Universitatis Carolinae. Mathematica et Physica
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Ivana Šebestová, V. Dolejší (2012)
Acta Universitatis Carolinae. Mathematica et Physica
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Ivana Šebestová (2014)
Applications of Mathematics
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We deal with the numerical solution of the nonstationary heat conduction equation with mixed Dirichlet/Neumann boundary conditions. The backward Euler method is employed for the time discretization and the interior penalty discontinuous Galerkin method for the space discretization. Assuming shape regularity, local quasi-uniformity, and transition conditions, we derive both a posteriori upper and lower error bounds. The analysis is based on the Helmholtz decomposition, the averaging interpolation...
Andrea Toselli (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We propose and analyze a domain decomposition method on non-matching grids for partial differential equations with non-negative characteristic form. No weak or strong continuity of the finite element functions, their normal derivatives, or linear combinations of the two is imposed across the boundaries of the subdomains. Instead, we employ suitable bilinear forms defined on the common interfaces, typical of discontinuous Galerkin approximations. We prove an error bound which is optimal...
Paola F. Antonietti, Blanca Ayuso (2007)
ESAIM: Mathematical Modelling and Numerical Analysis
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We propose and study some new additive, two-level non-overlapping Schwarz preconditioners for the solution of the algebraic linear systems arising from a wide class of discontinuous Galerkin approximations of elliptic problems that have been proposed up to now. In particular, two-level methods for both symmetric and non-symmetric schemes are introduced and some interesting features, which have no analog in the conforming case, are discussed. Both the construction and analysis of the...
Roland Becker, Peter Hansbo, Rolf Stenberg (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this note, we propose and analyse a method for handling interfaces between non-matching grids based on an approach suggested by Nitsche (1971) for the approximation of Dirichlet boundary conditions. The exposition is limited to self-adjoint elliptic problems, using Poisson’s equation as a model. A priori and a posteriori error estimates are given. Some numerical results are included.