Name
Title | ||
|---|---|---|
An Efficient Filtered Scheme for Some First Order Time-Dependent Hamilton-Jacobi Equations. |
Abstract | ||
|---|---|---|
We introduce a new class of “filtered” schemes for some first order nonlinear Hamilton--Jacobi equations. The work follows recent ideas of Froese and Oberman [SIAM J. Numer. Anal., 51 (2013), pp. 423--444] and Oberman and Salvador [J. Comput. Phys., 284 (2015), pp. 367--388] for steady equations. Here we mainly study the time-dependent setting and focus on fully explicit schemes. Furthermore, specific corrections to the filtering idea are also needed in order to obtain high-order accuracy. The proposed schemes are not monotone but still satisfy some $epsilon$-monotone property. A general convergence result together with a precise error estimate of order $sqrt{Delta x}$ are given ($Delta x$ is the mesh size). The framework allows us to construct finite difference discretizations that are easy to implement and high-order in the domain where the solution is smooth. A novel error estimate is also given in the case of the approximation of steady equations. Numerical tests including evolutive convex and non... |
Year | Venue | Field |
|---|---|---|
2016 | SIAM J. Scientific Computing | Convergence (routing),Mathematical optimization,Nonlinear system,First order,Mathematical analysis,Hamilton–Jacobi equation,Finite difference,Filter (signal processing),Regular polygon,Monotone polygon,Mathematics |
DocType | Volume | Issue |
Journal | 38 | 1 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Olivier Bokanowski | 1 | 98 | 12.07 |
| Maurizio Falcone | 2 | 235 | 19.89 |
| Smita Sahu | 3 | 0 | 0.34 |