5 papers
Convergence of Finite Element Methods for Ricci Flow
Guangwei Gao, Evan S. Gawlik, Buyang Li
The convergence of a finite element discretization for the two-dimensional Ricci flow is proved. In this method, the Ricci flow on a two-dimensional surface is formulated into solu…
Intrinsic Finite Element Error Analysis on Manifolds with Regge Metrics, with Application to Calculating Connection Forms
Evan S. Gawlik, Jack McKee
We present some aspects of the theory of finite element exterior calculus as applied to partial differential equations on manifolds, especially manifolds endowed with an approximat…
On the Curvature of Regge Metrics
Evan S. Gawlik, Jack McKee
We use moving frame techniques to derive a notion of curvature for a class of piecewise-smooth Riemannian metrics called Regge metrics, showing that it is a measure that simultaneo…
Structure-preserving and thermodynamically consistent finite element discretization for visco-resistive MHD with thermoelectric effect
Evan S. Gawlik, François Gay-Balmaz, Bastien Manach-Pérennou
We present a structure-preserving and thermodynamically consistent numerical scheme for classical magnetohydrodynamics, incorporating viscosity, magnetic resistivity, heat transfer…
Variational and thermodynamically consistent finite element discretization for heat conducting viscous fluids
Evan S. Gawlik, François Gay-Balmaz
Respecting the laws of thermodynamics is crucial for ensuring that numerical simulations of dynamical systems deliver physically relevant results. In this paper, we construct a str…