Related papers: High-order In-cell Discontinuous Reconstruction pa…
In this paper, we introduce a novel high-order shock tracking method and provide a proof of concept. Our method leverages concepts from implicit shock tracking and extended discontinuous Galerkin methods, primarily designed for solving…
The objective of this contribution is to compare two methods proposed recently in order to build efficient reduced-order models for geometrically nonlinear structures. The first method relies on the normal form theory that allows one to…
The hybrid high-order method is a modern numerical framework for the approximation of elliptic PDEs. We present here an extension of the hybrid high-order method to meshes possessing curved edges/faces. Such an extension allows us to…
In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may be relevant for the modelling of bird…
Diffusion models have advanced unsupervised anomaly detection by improving the transformation of pathological images into pseudo-healthy equivalents. Nonetheless, standard approaches may compromise critical information during pathology…
In this paper we present three different numerical approaches to account for curl-type involution constraints in hyperbolic partial differential equations for continuum physics. All approaches have a direct analogy to existing and…
Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
The application of suitable numerical boundary conditions for hyperbolic conservation laws on domains with complex geometry has become a problem with certain difficulty that has been tackled in different ways according to the nature of the…
The paper introduces a new way to construct dissipative solutions to a second order variational wave equation. By a variable transformation, from the nonlinear PDE one obtains a semilinear hyperbolic system with sources. In contrast with…
We study solutions to nonlinear hyperbolic systems with fully nonlinear relaxation terms in the limit of, both, infinitely stiff relaxation and arbitrary late time. In this limit, the dynamics is governed by effective systems of parabolic…
Since the discovery of the Harper-Hofstadter model, it has been known that condensed matter systems with periodic modulations can be promoted to non-trivial topological states with emergent gauge fields in higher dimensions. In this work,…
We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete unknowns that are polynomials attached to the faces and cells of a coarse mesh;…
We are interested in the high-order approximation of anisotropic, potential-driven advection-diffusion models on general polytopal partitions. We study two hybrid schemes, both built upon the Hybrid High-Order technology. The first one…
We propose a new family of high-order explicit generalized-$\alpha$ methods for hyperbolic problems with the feature of dissipation control. Our approach delivers $2k,\, \left(k \in \mathbb{N}\right)$ accuracy order in time by solving $k$…
In this paper, we design and analyze a Hybrid-High Order (HHO) approximation for a class of quasilinear elliptic problems of nonmonotone type. The proposed method has several advantages, for instance, it supports arbitrary order of…
We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is…
In this work, we introduce a new Hybrid High-Order method for the numerical simulation of fracture propagation based on phase-field models. The proposed method supports general meshes made of polygonal/polyhedral elements, which provides…
A high-order Flux reconstruction implementation of the hyperbolic formulation for the incompressible Navier-Stokes equation is presented. The governing equations employ Chorin's classical artificial compressibility (AC) formulation cast in…
Deep learning methods, which exploit auto-differentiation to compute derivatives without dispersion or dissipation errors, have recently emerged as a compelling alternative to classical mesh-based numerical schemes for solving hyperbolic…