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12/21/2022
Analysis of an Explicit, High-Order Semi-Lagrangian Nodal Method
A discrete analysis of the phase and dissipation errors of an explicit, ...
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03/21/2022
On the Theoretical Foundation of Overset Grid Methods for Hyperbolic Problems II: Entropy Bounded Formulations for Nonlinear Conservation Laws
We derive entropy conserving and entropy dissipative overlapping domain ...
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05/10/2021
On the Theoretical Foundation of Overset Grid Methods for Hyperbolic Problems: Well-Posedness and Conservation
We use the energy method to study the well-posedness of initial-boundary...
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12/11/2020
A Split-Form, Stable CG/DG-SEM for Wave Propagation Modeled by Linear Hyperbolic Systems
We present a hybrid continuous and discontinuous Galerkin spectral eleme...
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11/23/2020
Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps
We use the behavior of the L_2 norm of the solutions of linear hyperboli...
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05/05/2020
Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations
Discontinuous Galerkin (DG) methods have a long history in computational...
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10/24/2019
Entropy-stable discontinuous Galerkin approximation with summation-by-parts property for the incompressible Navier-Stokes/Cahn-Hilliard system
We develop an entropy stable two-phase incompressible Navier–Stokes/Cahn...
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08/12/2019
Naturally curved quadrilateral mesh generation using an adaptive spectral element solver
We describe an adaptive version of a method for generating valid natural...
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07/12/2019
Entropy-stable discontinuous Galerkin approximation with summation-by-parts property for the incompressible Navier-Stokes equations with variable density and artificial compres
We present a provably stable discontinuous Galerkin spectral element met...
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07/12/2019