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08/28/2023
Consistency and convergence of flux-corrected finite element methods for nonlinear hyperbolic problems
We investigate the consistency and convergence of flux-corrected finite ...
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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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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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12/22/2022
Fully well balanced entropy controlled DGSEM for shallow water flows: global flux quadrature and cell entropy correction
In this paper we propose a high order DGSEM formulation for balance laws...
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11/16/2022
A necessary condition for non oscillatory and positivity preserving time-integration schemes
Modified Patankar (MP) schemes are conservative, linear implicit and unc...
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11/02/2022
Entropy conservative high-order fluxes in the presence of boundaries
In this paper, we propose a novel development in the context of entropy ...
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10/30/2022
A new variable shape parameter strategy for RBF approximation using neural networks
The choice of the shape parameter highly effects the behaviour of radial...
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07/25/2022
On the convergence of residual distribution schemes for the compressible Euler equations via dissipative weak solutions
In this work, we prove the convergence of residual distribution schemes ...
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06/15/2022
On the Stability of Modified Patankar Methods
Patankar schemes have attracted more and more interests as a time-integr...
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06/08/2022
High order entropy preserving ADER scheme
In this paper, we develop a fully discrete entropy preserving ADER-Disco...
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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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03/10/2022
Summation-by-parts operators for general function spaces
Summation-by-parts (SBP) operators are popular building blocks for syste...
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03/01/2022
Comparison to control oscillations in high-order Finite Volume schemes via physical constraint limiters, neural networks and polynomial annihilation
The construction of high-order structure-preserving numerical schemes to...
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02/21/2022
Convergence of Discontinuous Galerkin Schemes for the Euler Equations via Dissipative Weak Solutions
In this paper, we present convergence analysis of high-order finite elem...
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10/26/2021
An Arbitrary High Order and Positivity Preserving Method for the Shallow Water Equations
In this paper, we develop and present an arbitrary high order well-balan...
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08/16/2021
A New Stability Approach for Positivity-Preserving Patankar-type Schemes
Patankar-type schemes are linearly implicit time integration methods des...
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06/09/2021
Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes
In [1] is proposed a simplified DeC method, that, when combined with the...
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01/24/2021
Towards Stable Radial Basis Function Methods for Linear Advection Problems
In this work, we investigate (energy) stability of global radial basis f...
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02/26/2020
DeC and ADER: Similarities, Differences and a Unified Framework
In this paper, we demonstrate that the ADER approach as it is used inter...
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02/26/2020
DeC and ADER: Similarities, Differences and an Unified Framework
In this paper, we demonstrate that the ADER approach as it is used inter...
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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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10/14/2019
General polytopial H(div) conformal finite elements and their discretisation spaces
We present a class of discretisation spaces and H(div)-conformal element...
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08/13/2019
Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes
For the general class of residual distribution (RD) schemes, including m...
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07/19/2019