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08/29/2023
Lie-Poisson Neural Networks (LPNets): Data-Based Computing of Hamiltonian Systems with Symmetries
An accurate data-based prediction of the long-term evolution of Hamilton...
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11/16/2022
Variational and thermodynamically consistent finite element discretization for heat conducting viscous fluids
Respecting the laws of thermodynamics is crucial for ensuring that numer...
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02/07/2022
Variational discretization of the Navier-Stokes-Fourier system
This paper presents the variational discretization of the compressible N...
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10/01/2021
Unified discrete multisymplectic Lagrangian formulation for hyperelastic solids and barotropic fluids
We present a geometric variational discretization of nonlinear elasticit...
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07/05/2021
Selective decay for the rotating shallow-water equations with a structure-preserving discretization
Numerical models of weather and climate critically depend on long-term s...
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05/03/2021
A structure-preserving finite element method for compressible ideal and resistive MHD
We construct a structure-preserving finite element method and time-stepp...
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02/22/2021
Multisymplectic variational integrators for barotropic and incompressible fluid models with constraints
We present a structure preserving discretization of the fundamental spac...
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12/08/2020
A Finite Element Method for MHD that Preserves Energy, Cross-Helicity, Magnetic Helicity, Incompressibility, and div B = 0
We construct a structure-preserving finite element method and time-stepp...
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10/13/2019
A Conservative Finite Element Method for the Incompressible Euler Equations with Variable Density
We construct a finite element discretization and time-stepping scheme fo...
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10/12/2019