We describe an algorithm for solving steady one-dimensional convex-like Hamilton-Jacobi equations using a L1-minimization technique on piecewise linear approximations. For a large class of convex Hamiltonians, the algorithm is proven to be convergent and of optimal complexity whenever the viscosity solution is q-semiconcave. Numerical results are presented to illustrate the performance of the method.
|Original language||English (US)|
|Number of pages||28|
|Journal||Communications in Mathematical Sciences|
|State||Published - 2009|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This material is based upon work supported by the National Science Foundation grant DMS-0510650.This publication is based on work supported by Award No. KUS-C1-016-04, made by King AbdullahUniversity of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.