Strong Convergence of Numerical Solutions to Degenerate Variational Problems
- 1 January 1995
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 64 (209) , 117-127
- https://doi.org/10.2307/2153325
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.
Keywords
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