%0 Journal Article %1 Kay2008Finite %A Kay, David %A Styles, Vanessa %A Welford, Richard %D 2008 %J Interfaces and Free Boundaries %K 35q30-navier-stokes-equations 76d05-incompressible-navier-stokes-equations 76m10-finite-element-methods-in-fluid-mechanics 82c24-time-dependent-statistical-mechanics-of-interface-problems cahn-hilliard cahn-hilliard-navier-stokes %P 15--43 %R 10.4171/ifb/178 %T Finite Element Approximation of a Cahn–Hilliard–Navier–Stokes System %U http://dx.doi.org/10.4171/ifb/178 %X We consider a semi-discrete and a practical fully-discrete finite element approximation of a Cahn–Hilliard–Navier–Stokes system. This system arises in the modelling of multiphase fluid systems. We show order h error estimate between the solution of the system and the solution of the semi-discrete approximation. We also show the convergence of the fully discrete approximation. Finally, we present an efficient implementation of the fully discrete scheme together with some numerical simulations.

@article{Kay2008Finite, abstract = {{We consider a semi-discrete and a practical fully-discrete finite element approximation of a Cahn–Hilliard–Navier–Stokes system. This system arises in the modelling of multiphase fluid systems. We show order h error estimate between the solution of the system and the solution of the semi-discrete approximation. We also show the convergence of the fully discrete approximation. Finally, we present an efficient implementation of the fully discrete scheme together with some numerical simulations.}}, added-at = {2019-03-01T00:11:50.000+0100}, author = {Kay, David and Styles, Vanessa and Welford, Richard}, biburl = {https://www.bibsonomy.org/bibtex/29056aa451be97747b8ffd512bddada6b/gdmcbain}, citeulike-article-id = {14615503}, citeulike-attachment-1 = {kay_08_finite.pdf; /pdf/user/gdmcbain/article/14615503/1140839/kay_08_finite.pdf; 68e8cc5ac728774416490a83d90ff71b7d511333}, citeulike-linkout-0 = {http://dx.doi.org/10.4171/ifb/178}, doi = {10.4171/ifb/178}, file = {kay_08_finite.pdf}, interhash = {a57e5772b8e1de724aeb146e3c2350ba}, intrahash = {9056aa451be97747b8ffd512bddada6b}, issn = {1463-9963}, journal = {Interfaces and Free Boundaries}, keywords = {35q30-navier-stokes-equations 76d05-incompressible-navier-stokes-equations 76m10-finite-element-methods-in-fluid-mechanics 82c24-time-dependent-statistical-mechanics-of-interface-problems cahn-hilliard cahn-hilliard-navier-stokes}, pages = {15--43}, posted-at = {2018-07-18 05:48:58}, priority = {5}, timestamp = {2019-03-01T00:11:50.000+0100}, title = {{Finite Element Approximation of a Cahn–Hilliard–Navier–Stokes System}}, url = {http://dx.doi.org/10.4171/ifb/178}, year = 2008 }