Error estimates for finite element methods for a wide-angle parabolic equation

Akrivis, GD; Dougalis, VA; Kampanis, NA

dc.contributor.author	Akrivis, GD	en
dc.contributor.author	Dougalis, VA	en
dc.contributor.author	Kampanis, NA	en
dc.date.accessioned	2014-03-01T01:42:34Z
dc.date.available	2014-03-01T01:42:34Z
dc.date.issued	1994	en
dc.identifier.issn	01689274	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/23872
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0003344387&partnerID=40&md5=db51a24d1a02345ab80c12cc5994f386	en
dc.title	Error estimates for finite element methods for a wide-angle parabolic equation	en
heal.type	journalArticle	en
heal.publicationDate	1994	en
heal.abstract	We consider a model initial-and boundary-value problem for the third-order wide-angle parabolic approximation of underwater acoustics with depth- and range-dependent coefficients. We discritize the problem in the depth variable by the standard Galerkin finite element method and prove optimal-order L2-error estimates for the ensuing continuous-in-range semidiscrete approximation. The associated ODE systems are then discretized in range, first by a second-order accurate Crank-Nicolson-type method, and then by the fourth-order, two-stage Gauss-Legendre, implicit Runge-Kutta scheme. We show that both these fully discrete methods are unconditionally stable and possess L2-error estimates of optimal rates. © 1994.	en
heal.journalName	Applied Numerical Mathematics	en
dc.identifier.volume	16	en
dc.identifier.issue	1-2	en
dc.identifier.spage	81	en
dc.identifier.epage	100	en