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Persistent URL http://purl.org/net/epubs/work/64110
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Record Id 64110
Title Interplay between discretization and algebraic computation in adaptive numerical solution of elliptic PDE problems
Abstract The Adaptive Finite Element Method (AFEM) for approximating solutions of PDE boundary value and eigenvalue problems is a numerical scheme that automatically and iteratively adapts the finite element space until a sufficiently accurate approximate solution is found. The adaptation process is based on a posteriori error estimators, and at each step of this process an algebraic problem (linear or nonlinear algebraic system or eigenvalue problem) has to be solved. In practical computations the solution of the algebraic problem cannot be obtained exactly. As a consequence, the algebraic error should be incorporated in the context of the AFEM and its a posteriori error estimators. The goal of this paper is to survey, with no claim for completeness, some existing approaches in the AFEM context that consider the interplay between the finite element discretization and the algebraic computation. We believe that a better understanding of this interplay is of great importance for the future development in the area of numerically solving large-scale real-world motivated problems.
Organisation STFC , SCI-COMP , SCI-COMP-CM
Keywords adaptive finite element methods , boundary value problems , eigenvalue problems , a posteriori error analysis , linear algebraic solvers , balancing of errors , stopping criteria MSC 2000 65F10 , 65F15 , 65N22 , 65N25 , 65N30
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Language English (EN)
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Report Final version before publication: revision of RAL-P-2012-006. AriLieMieStr13_final.pdf 2013