arXiv subjects

Alexandros Skouras

Publications and source records attributed to Alexandros Skouras.

2 recordsLinked to original sources

arXiv2026

A low-order hybrid method for the variable-density incompressible Navier-Stokes equations

In this work we introduce and analyse a new low-order method for the variable-density incompressible Navier-Stokes equations. The main novelty of the proposed method lies in the support of general meshes, possibly including polygonal or polyhedral elements as well as non-matching interfaces. We carry out a complete analysis, showing stability, existence and uniqueness of a discrete solution, and convergence of the latter to a suitably defined weak solution of the continuous problem. Numerical tests validate the theoretical results.

math.NA↗

arXiv2025

Existence of solution to a system of PDEs modeling the crystal growth inside lithium batteries

We study a model for lithium (Li) electrodeposition on Li-metal electrodes that leads to dendritic pattern formation. The model comprises of a system of three coupled PDEs, taking the form of an Allen--Cahn equation, a Nernst--Planck equation and a Poisson equation. We prove existence of a weak solution and stability results for this system and present numerical simulations resulting from a finite element approximation of the system, which illustrate the dendritic nature of solutions to the model.

math.AP↗