TY - JOUR
T1 - An optimal L1-minimization algorithm for stationary Hamilton-Jacobi equations
AU - Guermond, Jean-Luc
AU - Popov, Bojan
N1 - KAUST 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.
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/597541
UR - http://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0007/0001/a011/
UR - http://www.scopus.com/inward/record.url?scp=64549136293&partnerID=8YFLogxK
U2 - 10.4310/cms.2009.v7.n1.a11
DO - 10.4310/cms.2009.v7.n1.a11
M3 - Article
SN - 1539-6746
VL - 7
SP - 211
EP - 238
JO - Communications in Mathematical Sciences
JF - Communications in Mathematical Sciences
IS - 1
ER -