• English
    • Norsk
  • English 
    • English
    • Norsk
  • Administration
View Item 
  •   Home
  • Det matematisk-naturvitenskapelige fakultet
  • Matematisk institutt
  • Matematisk institutt
  • View Item
  •   Home
  • Det matematisk-naturvitenskapelige fakultet
  • Matematisk institutt
  • Matematisk institutt
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

A CONVERGENCE RATE FOR SEMI-DISCRETE SPLITTING APPROXIMATIONS FOR DEGENERATE PARABOLIC EQUATIONS WITH SOURCE TERMS

Jakobsen, Espen R.; Karlsen, Kenneth H.
Research report
View/Open
pm32-04.pdf (297.7Kb)
Year
2004
Permanent link
http://urn.nb.no/URN:NBN:no-23680

Is part of
Preprint series. Pure mathematics
Metadata
Show metadata
Appears in the following Collection
  • Matematisk institutt [1973]
Abstract
We study a semi-discrete splitting method for computing approximate viscosity solutions of the initial value problem for a class of nonlinear degenerate parabolic equations with source terms. It is fairly standard to prove that the semi-discrete splitting approximations converge to the desired viscosity solution as the splitting step $\Dt$ tends to zero. The purpose of this paper is, however, to consider the more difficult problem of providing a precise estimate of the convergence rate. Using viscosity solution techniques we establish the $L^{\infty}$ convergence rate $\mathcal{O}(\sqrt{\Dt})$ for the approximate solutions, and this estimate is robust with respect to the regularity of the solutions. We also provide an extension of this result to weakly coupled systems of equations, and in the case of more regular solutions we recover the ''classical'' rate $\mathcal{O}(\Dt)$. Finally, we analyze in an example a fully discrete splitting method.
 
Responsible for this website 
University of Oslo Library


Contact Us 
duo-hjelp@ub.uio.no


Privacy policy
 

 

For students / employeesSubmit master thesisTemplatesAccess to restricted material

Browse

All of DUOCommunities & CollectionsBy Issue DateAuthorsTitlesThis CollectionBy Issue DateAuthorsTitles

For library staff

Login

Statistics

View Usage Statistics
RSS Feeds
 
Responsible for this website 
University of Oslo Library


Contact Us 
duo-hjelp@ub.uio.no


Privacy policy