Algorithmic approach to strong consistency analysis of finite difference approximations to PDE systems
dc.contributor.author | Gerdt, VP | |
dc.contributor.author | Robertz, Daniel | |
dc.date.accessioned | 2019-05-11T17:53:21Z | |
dc.date.issued | 2019-07-08 | |
dc.identifier.uri | http://hdl.handle.net/10026.1/13826 | |
dc.description.abstract |
For a wide class of polynomially nonlinear systems of partial differential equations we suggest an algorithmic approach to the s(trong)-consistency analysis of their finite difference approximations on Cartesian grids. First we apply the differential Thomas decomposition to the input system, resulting in a partition of the solution set. We consider the output simple subsystem that contains a solution of interest. Then, for this subsystem, we suggest an algorithm for verification of s-consistency for its finite difference approximation. For this purpose we develop a difference analogue of the differential Thomas decomposition, both of which jointly allow to verify the s-consistency of the approximation. As an application of our approach, we show how to produce s-consistent difference approximations to the incompressible Navier-Stokes equations including the pressure Poisson equation. | |
dc.format.extent | 163-170 | |
dc.language.iso | en | |
dc.publisher | ACM | |
dc.subject | cs.SC | |
dc.subject | cs.SC | |
dc.subject | math.AP | |
dc.subject | math.NA | |
dc.subject | math.RA | |
dc.title | Algorithmic approach to strong consistency analysis of finite difference approximations to PDE systems | |
dc.type | journal-article | |
dc.type | Conference Proceeding | |
plymouth.author-url | http://arxiv.org/abs/1904.12912v1 | |
plymouth.publication-status | Published | |
plymouth.journal | Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC | |
dc.identifier.doi | 10.1145/3326229.3326255 | |
plymouth.organisational-group | /Plymouth | |
plymouth.organisational-group | /Plymouth/Faculty of Science and Engineering | |
plymouth.organisational-group | /Plymouth/Faculty of Science and Engineering/School of Engineering, Computing and Mathematics | |
plymouth.organisational-group | /Plymouth/Users by role | |
plymouth.organisational-group | /Plymouth/Users by role/Academics | |
dcterms.dateAccepted | 2019-04-02 | |
dc.rights.embargodate | 2023-7-19 | |
dc.rights.embargoperiod | Not known | |
rioxxterms.versionofrecord | 10.1145/3326229.3326255 | |
rioxxterms.licenseref.uri | http://www.rioxx.net/licenses/all-rights-reserved | |
rioxxterms.type | Journal Article/Review |