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.
Publication Date
2019-07-08
Publication Title
Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
Publisher
ACM
Embargo Period
2024-11-22
Additional Links
http://arxiv.org/abs/1904.12912v1
Keywords
cs.SC, cs.SC, math.AP, math.NA, math.RA
Recommended Citation
Gerdt, V., & Robertz, D. (2019) 'Algorithmic approach to strong consistency analysis of finite difference approximations to PDE systems', Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, . ACM: Retrieved from https://pearl.plymouth.ac.uk/secam-research/1769
