GALERKIN PROJECTIONS AND THE PROPER ORTHOGONAL DECOMPOSITION FOR EQUIVARIANT EQUATIONS

abstract

• In this paper we are interested in Galerkin projections of certain partial differential evolution equations, that retain the symmetries of the original nontruncated equations. In particular, we extend several results concerning the Galerkin projections, based on the proper orthogonal decomposition (which is also known as the Karhunen-Love expansion) for equations which are equivariant under the action of compact Abelian symmetry groups. We provide sufficient conditions for numerical schemes, based on the linear and the nonlinear Galerkin method, to retain the symmetries of the original system. We perform a rational analysis of methods which use symmetry to enlarge the ensemble size of a data set. Our analysis has the potential for computational savings. 1993.

authors

• Titi, Edriss

published proceedings

• PHYSICS LETTERS A

author list (cited authors)

• BERKOOZ, G., & TITI, E. S.

citation count

• 41

complete list of authors

• BERKOOZ, G||TITI, ES

publication date

• March 1993

publisher

• Elsevier  Publisher

published in

• Physics Letters, Section A: General, Atomic and Solid State Physics  Journal

keywords

• 49 Mathematical Sciences
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1016/0375-9601(93)90549-F

start page

• 94

end page

• 102

volume

• 174

issue

• 1-2

URL

• http://dx.doi.org/10.1016/0375-9601(93)90549-f