Name
Title | ||
|---|---|---|
Stability And Convergence Of Second Order Backward Differentiation Schemes For Parabolic Hamilton-Jacobi-Bellman Equations |
Abstract | ||
|---|---|---|
We study a second order Backward Differentiation Formula (BDF) scheme for the numerical approximation of linear parabolic equations and nonlinear Hamilton-Jacobi-Bellman (HJB) equations. The lack of monotonicity of the BDF scheme prevents the use ofwell-known convergence results for solutions in the viscosity sense. We first consider one-dimensional uniformly parabolic equations and prove stability with respect to perturbations, in the L-2 norm for linear and semi-linear equations, and in the H-1 norm for fully nonlinear equations of HJB and Isaacs type. These results are then extended to two-dimensional semi-linear equations and linear equations with possible degeneracy. From these stability results we deduce error estimates in L-2 norm for classical solutions to uniformly parabolic semi-linear HJB equations, with an order that depends on their Holder regularity, while full second order is recovered in the smooth case. Numerical tests for the Eikonal equation and a controlled diffusion equation illustrate the practical accuracy of the scheme in different norms. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1007/s00211-021-01202-x | NUMERISCHE MATHEMATIK |
DocType | Volume | Issue |
Journal | 148 | 1 |
ISSN | Citations | PageRank |
0029-599X | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Olivier Bokanowski | 1 | 98 | 12.07 |
| Athena Picarelli | 2 | 12 | 1.82 |
| Christoph Reisinger | 3 | 46 | 10.27 |