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01/05/2023
Finite element approximation of scalar curvature in arbitrary dimension
We analyze finite element discretizations of scalar curvature in dimensi...
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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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11/03/2021
Finite element approximation of the Levi-Civita connection and its curvature in two dimensions
We construct finite element approximations of the Levi-Civita connection...
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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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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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11/25/2020
Iterations for the Unitary Sign Decomposition and the Unitary Eigendecomposition
We construct fast, structure-preserving iterations for computing the sig...
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11/21/2020
Zolotarev's fifth and sixth problems
In an influential 1877 paper, Zolotarev asked and answered four question...
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11/01/2020
Local Finite Element Approximation of Sobolev Differential Forms
We address fundamental aspects in the approximation theory of vector-val...
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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
A Variational Finite Element Discretization of Compressible Flow
We present a finite element variational integrator for compressible flow...
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06/26/2019