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We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…
We introduce a nonlinear structure preserving high-order scheme for anisotropic advection-diffusion equations. This scheme, based on Hybrid High-Order methods, can handle general meshes. It also has an entropy structure, and preserves the…
There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which…
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…
Godunov type numerical schemes for the class of hyperbolic systems, admitting non-classical $\delta-$ shocks are proposed. It is shown that the numerical approximations converge to the solution and preserve the physical properties of the…
In this paper, we propose a class of non-oscillatory, entropy-stable discontinuous Galerkin (NOES-DG) schemes for solving hyperbolic conservation laws. By incorporating a specific form of artificial viscosity, our new scheme directly…
Jump penalty stabilisation techniques have been recently proposed for continuous and discontinuous high order Galerkin schemes [1,2,3]. The stabilisation relies on the gradient or solution discontinuity at element interfaces to incorporate…
In the Reduced Basis approximation of Stokes and Navier-Stokes problems, the Galerkin projection on the reduced spaces does not necessarily preserved the inf-sup stability even if the snapshots were generated through a stable full order…
We present a new perspective on the use of weighted essentially nonoscillatory (WENO) reconstructions in high-order methods for scalar hyperbolic conservation laws. The main focus of this work is on nonlinear stabilization of continuous…
We introduce an adaptive viscosity regularization approach for the numerical solution of systems of nonlinear conservation laws with shock waves. The approach seeks to solve a sequence of regularized problems consisting of the system of…
In this paper, we introduce a hyperbolic model for entropy dissipative system of viscous conservation laws via a flux relaxation approach. We develop numerical schemes for the resulting hyperbolic relaxation system by employing the…
For scalar conservation laws, we prove that spectrally stable stationary Lax discrete shock profiles are nonlinearly stable in some polynomially-weighted $\ell^1$ and $\ell^\infty$ spaces. In comparison with several previous nonlinear…
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant…
A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed formulation fits within the framework of the finite cell method, where essential…
This work provides a comparative assessment of several low-dissipation numerical schemes for hyperbolic conservation laws, highlighting their performance relative to the classical Harten-Lax-van Leer (HLL) schemes. The schemes under…
We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…
The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging…
Variable viscosity arises in many flow scenarios, often imposing numerical challenges. Yet, discretisation methods designed specifically for non-constant viscosity are few, and their analysis is even scarcer. In finite element methods for…
The nonlinear convection terms in the governing equations of compressible fluid flows are hyperbolic in nature and are nontrivial for modelling and numerical simulation. Many numerical methods have been developed in the last few decades for…
We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the…