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05/08/2023
A fully conservative and shift-invariant formulation for Galerkin discretizations of incompressible variable density flow
This paper introduces a formulation of the variable density incompressib...
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09/20/2022
A high-order artificial compressibility method based on Taylor series time-stepping for variable density flow
In this paper, we introduce a fourth-order accurate finite element metho...
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06/20/2022
Monolithic parabolic regularization of the MHD equations and entropy principles
We show at the PDE level that the monolithic parabolic regularization of...
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12/16/2021
A high-order residual-based viscosity finite element method for the ideal MHD equations
We present a high order, robust, and stable shock-capturing technique fo...
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11/22/2021
A finite element based Heterogeneous Multiscale Method for the Landau-Lifshitz equation
We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equ...
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10/27/2021
Stability estimates for radial basis function methods applied to time-dependent hyperbolic PDEs
We derive stability estimates for three commonly used radial basis funct...
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09/15/2021
Residual viscosity stabilized RBF-FD methods for solving nonlinear conservation laws
We formulate an oversampled radial basis function generated finite diffe...
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03/12/2021
Energy stable and accurate coupling of finite element methods and finite difference methods
We introduce a hybrid method to couple continuous Galerkin finite elemen...
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06/01/2020