Thursday, February 29, 9:30 am in room MTH 3206, University of Maryland,
College Park
A nonlinear Galerkin method in the collocation case
Dr. Lucia Dettori
Division of Applied Mathematics, Brown University and Dept. of
Mathematics & Statistics, University of Maryland Baltimore County
lucia@math.umbc.edu
In this talk we present the implementation of the Nonlinear Galerkin
method with collocation discretizations based on Fourier and Chebyshev
aproximations. The nonlinear Galerkin method is a multiresolution method
stemming from the theory of inertial manifolds. It is based on
decompositions of the unknown into two arrays of unknowns, which
represent respectively the large scale component and the small scale
component of the solution. Such a decomposition is accomplished via the
splitting of the fine grid into two coarse grids. This produces interesting
connections between the physical space and the Fourier/Chebyshev space
representation of the function. The method is applied to a nonlinear
parabolic equation; its stability is proved and implementation issues
are discussed, showing the advantages of the method.
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