Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Strong convergence of numerical solutions to degenerate variational problems

Authors: R. A. Nicolaides and Noel J. Walkington
Journal: Math. Comp. 64 (1995), 117-127
MSC: Primary 65N15; Secondary 65K10, 65N12
MathSciNet review: 1262281
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Numerical approximations of strongly degenerate variational problems of the form $ J(u) = \smallint _0^1F(u' ) + {(u - f)^2}$ are considered, where F is assumed convex but may have intervals where $ F'' = 0$. It is shown that, in spite of the degeneracy, natural numerical approximations still converge in $ {W^{1,p}}$. Rates in weaker norms and the connection with nonconvex variational problems are also considered.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N15, 65K10, 65N12

Retrieve articles in all journals with MSC: 65N15, 65K10, 65N12

Additional Information

Keywords: Approximation of degenerate variational problems
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society