Work

Energy conserving compatible space--time FEM for deterministic and stochastic rotating shallow water

Year: 2026

Type: preprint

Abstract: We present a fully discrete energy conserving discretisation of the rotating shallow water equations with arbitrary order in space and time. A space time finite element discretisation is used, built from compatible finite element methods in space and continuous Petrov-Galerkin schemes in time. Projected auxiliary variables for Hamiltonian derivatives are necessary for exact energy conservation. We provide an iterative solver approach based on monolithic patch smoothers, which allows us to efficiently converge a Newton method sufficiently that energy errors due to the solver are very small. We extend this construction to the energy conserving Stochastic Forcing by Lie Transport formulation. Then we demonstrate the convergence, conservation and robustness in numerical tests.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.13624

Authors: Singh, Maneesh Kumar, Cotter, Colin J.

Institutions: SRM Institute of Science and Technology, Imperial College London

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Award: Next generation particle filters for stochastic partial differential equations

OpenAlex ID: W7221510976

Cites: 5

Cited by:

Related to: 10