Year: 2010
Communications in Computational Physics, Vol. 8 (2010), Iss. 2 : pp. 445–470
Abstract
We consider in this paper a high-order, semi-Lagrangian technique to treat possibly degenerate advection-diffusion equations, which has been proposed in similar forms by various authors. The scheme is based on a stochastic representation formula for the solution, which allows to avoid the splitting between advective and diffusive part of the evolution operator. A general theoretical analysis is carried out in the paper, with a special emphasis on the possibility of using large Courant numbers, and numerical tests in one and two space dimensions are presented.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.070709.011209a
Communications in Computational Physics, Vol. 8 (2010), Iss. 2 : pp. 445–470
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
-
Semi-Lagrangian discontinuous Galerkin schemes for some first- and second-order partial differential equations
Bokanowski, Olivier | Simarmata, GiorevinusESAIM: Mathematical Modelling and Numerical Analysis, Vol. 50 (2016), Iss. 6 P.1699
https://doi.org/10.1051/m2an/2016004 [Citations: 4] -
Some Non-monotone Schemes for Time Dependent Hamilton–Jacobi–Bellman Equations in Stochastic Control
Warin, Xavier
Journal of Scientific Computing, Vol. 66 (2016), Iss. 3 P.1122
https://doi.org/10.1007/s10915-015-0057-9 [Citations: 7] -
Analysis of the Monte-Carlo Error in a Hybrid Semi-Lagrangian Scheme
Bréhier, Charles-Edouard | Faou, ErwanApplied Mathematics Research eXpress, Vol. 2015 (2015), Iss. 2 P.167
https://doi.org/10.1093/amrx/abv001 [Citations: 1] -
Multigrid Methods for Second Order Hamilton--Jacobi--Bellman and Hamilton--Jacobi--Bellman--Isaacs Equations
Han, Dong | Wan, Justin W. L.SIAM Journal on Scientific Computing, Vol. 35 (2013), Iss. 5 P.S323
https://doi.org/10.1137/120881476 [Citations: 10] -
A high-order scheme for mean field games
Calzola, Elisa | Carlini, Elisabetta | Silva, Francisco J.Journal of Computational and Applied Mathematics, Vol. 445 (2024), Iss. P.115769
https://doi.org/10.1016/j.cam.2024.115769 [Citations: 0] -
A fully semi-Lagrangian discretization for the 2D incompressible Navier–Stokes equations in the vorticity-streamfunction formulation
Bonaventura, Luca | Ferretti, Roberto | Rocchi, LorenzoApplied Mathematics and Computation, Vol. 323 (2018), Iss. P.132
https://doi.org/10.1016/j.amc.2017.11.030 [Citations: 12] -
Second Order Fully Semi-Lagrangian Discretizations of Advection-Diffusion-Reaction Systems
Bonaventura, Luca | Calzola, Elisa | Carlini, Elisabetta | Ferretti, RobertoJournal of Scientific Computing, Vol. 88 (2021), Iss. 1
https://doi.org/10.1007/s10915-021-01518-8 [Citations: 8] -
A Semi-Lagrangian scheme for the Fokker-Planck equation
Carlini, E. | Silva, F.J.IFAC-PapersOnLine, Vol. 49 (2016), Iss. 8 P.272
https://doi.org/10.1016/j.ifacol.2016.07.453 [Citations: 6] -
A semi-Lagrangian scheme for the game p-Laplacian via p-averaging
Falcone, M. | Finzi Vita, S. | Giorgi, T. | Smits, R.G.Applied Numerical Mathematics, Vol. 73 (2013), Iss. P.63
https://doi.org/10.1016/j.apnum.2012.11.006 [Citations: 11] -
Semi-Lagrangian Methods for Parabolic Problems in Divergence Form
Bonaventura, L. | Ferretti, R.SIAM Journal on Scientific Computing, Vol. 36 (2014), Iss. 5 P.A2458
https://doi.org/10.1137/140969713 [Citations: 16] -
Stochastic Optimal Control of a Sailboat
Miles, Cole | Vladimirsky, AlexanderIEEE Control Systems Letters, Vol. 6 (2022), Iss. P.2048
https://doi.org/10.1109/LCSYS.2021.3136438 [Citations: 2] -
Flux form Semi-Lagrangian methods for parabolic problems
Bonaventura, Luca | Ferretti, RobertoCommunications in Applied and Industrial Mathematics, Vol. 7 (2016), Iss. 3 P.56
https://doi.org/10.1515/caim-2016-0022 [Citations: 0] -
Risk-Aware Stochastic Control of a Sailboat
Wang, MingYi | Patnaik, Natasha | Somalwar, Anne | Wu, Jingyi | Vladimirsky, Alexander2024 American Control Conference (ACC), (2024), P.5460
https://doi.org/10.23919/ACC60939.2024.10644458 [Citations: 0] -
A scheme for the game p-Laplacian and its application to image inpainting
Carlini, Elisabetta | Tozza, SilviaApplied Mathematics and Computation, Vol. 461 (2024), Iss. P.128299
https://doi.org/10.1016/j.amc.2023.128299 [Citations: 0]