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08/07/2023
Friedrichs' systems discretized with the Discontinuous Galerkin method: domain decomposable model order reduction and Graph Neural Networks approximating vanishing viscosity so
Friedrichs' systems (FS) are symmetric positive linear systems of first-...
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08/03/2023
An optimisation-based domain-decomposition reduced order model for parameter-dependent non-stationary fluid dynamics problems
In this work, we address parametric non-stationary fluid dynamics proble...
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05/22/2023
On improving the efficiency of ADER methods
The (modern) arbitrary derivative (ADER) approach is a popular technique...
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12/15/2022
Efficient iterative arbitrary high order methods: an adaptive bridge between low and high order
We propose a new paradigm for designing efficient p-adaptive arbitrary h...
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11/26/2022
An optimisation-based domain-decomposition reduced order model for the incompressible Navier-Stokes equations
The aim of this work is to present a model reduction technique in the fr...
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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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10/06/2022
A new efficient explicit Deferred Correction framework: analysis and applications to hyperbolic PDEs and adaptivity
The Deferred Correction is an iterative procedure used to design numeric...
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06/13/2022
Spectral analysis of high order continuous FEM for hyperbolic PDEs on triangular meshes: influence of approximation, stabilization, and time-stepping
In this work we study various continuous finite element discretization f...
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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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05/26/2022
Arbitrary High Order WENO Finite Volume Scheme with Flux Globalization for Moving Equilibria Preservation
In the context of preserving stationary states, e.g. lake at rest and mo...
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12/20/2021
Model order reduction strategies for weakly dispersive waves
We focus on the numerical modelling of water waves by means of depth ave...
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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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09/21/2021
Analytical travelling vortex solutions of hyperbolic equations for validating very high order schemes
Testing the order of accuracy of (very) high order methods for shallow w...
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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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03/30/2021
Spectral analysis of continuous FEM for hyperbolic PDEs: influence of approximation, stabilization, and time-stepping
We study continuous finite element dicretizations for one dimensional hy...
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03/30/2020
Model Reduction for Advection Dominated Hyperbolic Problems in an ALE Framework: Offline and Online Phases
Model order reduction (MOR) techniques have always struggled in compress...
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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