3 papers
math.NA2026
Toward generalized solutions of the Keller--Segel equations with singular sensitivity and signal absorption via an algebraic manipulation finite element algorithm
Juan Vicente Gutiérrez-Santacreu
The paper that follows describes a numerical algorithm to solve the parabolic-parabolic Keller--Segel system characterized by singular sensitivity and signal absorption in such a m…
math.NA2025
Finite element approximation and very weak solution existence in a two-dimensional, degenerate Keller-Segel model
Juan Vicente Gutiérrez-Santacreu
This paper is devoted to the design and analysis of a numerical algorithm for approximating solutions of a degenerate cross-diffusion system, which models particular instances of t…
math.NA2024
Physics-based stabilized finite element approximations of the Poisson--Nernst--Planck equations
Jesús Bonilla, Juan Vicente Gutiérrez-Santacreu
We present and analyze two stabilized finite element methods for solving numerically the Poisson--Nernst--Planck equations. The stabilization we consider is carried out by using a…