相关论文: High-order In-cell Discontinuous Reconstruction pa…

We introduce novel high order well-balanced finite volume methods for the full compressible Euler system with gravity source term. They require no a priori knowledge of the hydrostatic solution which is to be well-balanced and are not…

We present a novel methodology for constructing arbitrarily high-order structure-preserving methods tailored for damped Hamiltonian systems. This method combines the idea of exponential integrator and energy-preserving collocation methods,…

Longstanding problems regarding the causality of the diffusion equation are resolved through a class of exact solutions. A universal differential solution for diffusive processes is derived that is causal and exact at any analytic point in…

In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and non-decreasing initial data. We remark that these…

In this paper, we propose a new unified first order hyperbolic model of Newtonian continuum mechanics coupled with electro-dynamics. The model is able to describe the behavior of moving elasto-plastic dielectric solids as well as viscous…

Many entropy-conservative and entropy-stable (summarized as entropy-preserving) methods for hyperbolic conservation laws rely on Tadmor's theory for two-point entropy-preserving numerical fluxes and its higher-order extension via flux…

In this paper, we present two different approaches for constructing reduced-order models (ROMs) for the two-dimensional shallow water equation (SWE). The first one is based on the noncanonical Hamiltonian/Poisson form of the SWE. After…

In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…

In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…

We propose a limiting procedure to preserve invariant domains with time explicit discrete high-order spectral discontinuous approximate solutions to hyperbolic systems of conservation laws. Provided the scheme is discretely conservative and…

In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…

We introduce an approximation technique for nonlinear hyperbolic systems with sources that is invariant domain preserving. The method is discretization-independent provided elementary symmetry and skew-symmetry properties are satisfied by…

Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques…

We present well-balanced, high-order, semi-discrete numerical schemes for one-dimensional blood flow models with discontinuous mechanical properties and algebraic source terms representing friction and gravity. While discontinuities in…

We are concerned with the time decay rates of strong solutions to a non-conservative compressible viscous two-phase fluid model in the whole space R3. Compared to the previous related works, the main novelty of this paper lies in the fact…

We introduce stabilized spline collocation schemes for the numerical solution of nonlinear, hyperbolic conservation laws. A nonlinear, residual-based viscosity stabilization is combined with a projection stabilization-inspired linear…

We present a higher-order extension of the dual cell method for the time-domain Maxwell equations in three spatial dimensions. The approach builds upon a variational reinterpretation of the Finite Integration Technique on dual meshes and…

In this paper we present two semi-implicit-type second order Compact Approximate Taylor (CAT2) numerical schemes and blend them with a local a posteriori Multi-dimensional Optimal Order Detection (MOOD) paradigm to solve hyperbolic systems…

The increasing penetration of renewable energy sources, characterised by low inertia and intermittent disturbances, presents substantial challenges to power system stability. As critical indicators of system stability, frequency dynamics…

In the present work, we consider multi-scale computation and convergence for nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells possessing temperature-dependent material properties and orthogonal periodic…