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07/26/2023
A superconvergent stencil-adaptive SBP-SAT finite difference scheme
A stencil-adaptive SBP-SAT finite difference scheme is shown to display ...
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07/10/2023
A symmetry and Noether charge preserving discretization of initial value problems
Taking insight from the theory of general relativity, where space and ti...
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06/28/2023
Summation-by-parts operators for general function spaces: The second derivative
Many applications rely on solving time-dependent partial differential eq...
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06/03/2023
A provably stable and high-order accurate finite difference approximation for the incompressible boundary layer equations
In this article we develop a high order accurate method to solve the inc...
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06/02/2023
Nonlinear Boundary Conditions for Initial Boundary Value Problems with Applications in Computational Fluid Dynamics
We derive new boundary conditions and implementation procedures for nonl...
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05/29/2023
Encapsulated generalized summation-by-parts formulations for curvilinear and non-conforming meshes
We extend the construction of so-called encapsulated global summation-by...
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02/13/2023
A method-of-lines framework for energy stable arbitrary Lagrangian-Eulerian methods
We present a novel framework based on semi-bounded spatial operators for...
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01/30/2023
Multi-dimensional summation-by-parts operators for general function spaces: Theory and construction
Summation-by-parts (SBP) operators allow us to systematically develop en...
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01/11/2023
Nonlinear Boundary Conditions for Energy and Entropy Stable Initial Boundary Value Problems in Computational Fluid Dynamics
We derive new boundary conditions and implementation procedures for nonl...
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05/27/2022
A new discretization technique for initial value problems based on a variational principle
Motivated by the fact that both the classical and quantum description of...
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04/07/2022
Energy-stable global radial basis function methods on summation-by-parts form
Radial basis function methods are powerful tools in numerical analysis a...
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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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03/10/2022
Summation-by-parts operators for general function spaces
Summation-by-parts (SBP) operators are popular building blocks for syste...
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01/14/2022
A new energy stable formulation of the compressible Euler equations
We show that a specific skew-symmetric form of hyperbolic problems leads...
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09/21/2021
Nonlinear and Linearised Primal and Dual Initial Boundary Value Problems: When are they Bounded? How are they Connected?
Linearisation is often used as a first step in the analysis of nonlinear...
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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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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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07/14/2020
Stable filtering procedures for nodal discontinuous Galerkin methods
We prove that the most common filtering procedure for nodal discontinuou...
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03/09/2020
A Class of A Stable Summation by Parts Time Integration Schemes
Since integration by parts is an important tool when deriving energy or ...
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12/18/2019
Analysis of the SBP-SAT Stabilization for Finite Element Methods Part II: Entropy Stability
In the research community, there exists the strong belief that a continu...
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12/17/2019
Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear problems
A pure Galerkin scheme is notoriously unstable. To remedy this issue, st...
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07/24/2019