A general framework for deriving integral preserving numerical methods for PDEs
It provides a general approach for preserving invariants in numerical PDE solvers, but the results are incremental and limited to polynomial nonlinearities.
The paper presents a general framework for constructing conservative numerical integrators for time-dependent PDEs, achieving second-order convergence. The method is applied to a test case with numerical validation.
A general procedure for constructing conservative numerical integrators for time dependent partial differential equations is presented. In particular, linearly implicit methods preserving a time discretised version of the invariant is developed for systems of partial differential equations with polynomial nonlinearities. The framework is rather general and allows for an arbitrary number of dependent and independent variables with derivatives of any order. It is proved formally that second order convergence is obtained. The procedure is applied to a test case and numerical experiments are provided.