Dr. Boris Andrews, University of Oxford

Shipeng Mao, Professor

Constructing conservative and dissipative integrators via auxiliary variables

16:00-17:00 January 21(Wednesday), S813

In this talk, we introduce a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of PDE and ODE initial value problems. The key idea is the representation of each conservation law or dissipation inequality by means of a certain "associated test function", which is then introduced into the discretisation as an auxiliary variable.

We will demonstrate the framework by its application to the Benjamin–Bona–Mahony and Cahn–Hilliard equations. Further applications discussed include novel structure-preserving integrators for the compressible Navier–Stokes equations, general conservative ODEs with arbitrarily many invariants, and the Boltzmann equation.