QA211 : Adaptive Variational Multiscale Methods
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2013
Authors:
Abstarct: We develop a new adaptive multiscale finite element method using the variational
multiscale frxamework together with a systematic technique for approximation of the fine
scale part of the solution. The fine scale is approximated by a sum of solutions to decoupled
localized problems, which are solved numerically. We derive an a posteriori error estimate
in the energy norm which captures the dependency of the crucial discretization parameters:
the coarse grid mesh size, the fine grid mesh size, and the sizes of the patches. baxsed on
the a posteriori error estimate we present an adaptive algorithm that automatically tunes
these parameters. Finally, we show how the method works in practice by presenting various
numerical examples.
Keywords:
#alerkin #duality #a posteriori error estimation #adaptivity #variational multiscale method #homogeneous #cell problem #periodic #localized problem Link
Keeping place: Central Library of Shahrood University
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Keeping place: Central Library of Shahrood University
Visitor: