##### Department of Mathematics,

University of California San Diego

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### Center for Computational Mathematics Seminar

## Ari Stern

#### Washington University in St. Louis

## Functional equivariance and conservation laws in numerical integration

##### Abstract:

Preservation of linear and quadratic invariants by numerical integrators has been well studied. However, many systems have linear or quadratic observables that are not invariant, but which satisfy evolution equations expressing important properties of the system. For example, a time-evolution PDE may have an observable that satisfies a local conservation law, such as the multisymplectic conservation law for Hamiltonian PDEs.

We introduce the concept of functional equivariance, a natural sense in which a numerical integrator may preserve the dynamics satisfied by certain classes of observables, whether or not they are invariant. After developing the general framework, we use it to obtain results on methods preserving local conservation laws in PDEs. In particular, integrators preserving quadratic invariants also preserve local conservation laws for quadratic observables, and symplectic integrators are multisymplectic.

### May 24, 2022

### 11:00 AM

AP&M 2402

Zoom ID 954 6624 3503

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