Communications in Mathematical Sciences
Volume 7 (2009)
An optimal L1-minimization algorithm for stationary Hamilton-Jacobi equations
Pages: 211 – 238
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.
Finite elements; best L1-approximation; viscosity solution; HJ equation; eikonal equation
2010 Mathematics Subject Classification
35J05, 65F05, 65N22, 65N35