Approximation of solutions of Hamilton-Jacobi equations on the Heisenberg group
Yves Achdou, Italo Capuzzo-Dolcetta (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
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We propose and analyze numerical schemes for viscosity solutions of time-dependent Hamilton-Jacobi equations on the Heisenberg group. The main idea is to construct a grid compatible with the noncommutative group geometry. Under suitable assumptions on the data, the Hamiltonian and the parameters for the discrete first order scheme, we prove that the error between the viscosity solution computed at the grid nodes and the solution of the discrete problem behaves like where is the mesh...