Bean, N.Lewis, A.Nguyen, G.T.O'Reilly, M.M.Sunkara, V.2022-06-212022-06-212022Methodology and Computing in Applied Probability, 2022; 24(4):2823-28641387-58411573-7713https://hdl.handle.net/2440/135534Published online: 23 May 2022The stochastic fluid-fluid model (SFFM) is a Markov process {(Xt,Yt,φt),t≥0}, where {φt,t≥0} is a continuous-time Markov chain, the first fluid, {Xt,t≥0}, is a classical stochastic fluid process driven by {φt,t≥0}, and the second fluid, {Yt,t≥0}, is driven by the pair {(Xt,φt),t≥0}. Operator-analytic expressions for the stationary distribution of the SFFM, in terms of the infinitesimal generator of the process {(Xt,φt),t≥0}, are known. However, these operator-analytic expressions do not lend themselves to direct computation. In this paper the discontinuous Galerkin (DG) method is used to construct approximations to these operators, in the form of finite dimensional matrices, to enable computation. The DG approximations are used to construct approximations to the stationary distribution of the SFFM, and results are verified by simulation. The numerics demonstrate that the DG scheme can have a superior rate of convergence compared to other methods.en© The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.Stochastic fluid-fluid processesStationary distributionDiscontinuous Galerkin methodJournal article10.1007/s11009-022-09945-22022-06-20458155Bean, N. [0000-0002-5351-3104]Lewis, A. [0000-0002-6785-3097]