56 citations · 112 across the 7 of their papers we have counts for
7 papers
Exploring numerical blow-up phenomena for the Keller-Segel-Navier-Stokes equations
Jesús Bonilla, Juan Vicente Gutiérrez-Santacreu
The Keller-Segel-Navier-Stokes system governs chemotaxis in liquid environments. This system is to be solved for the organism and chemoattractant densities and for the fluid veloci…
Bound-preserving finite element approximations of the Keller-Segel equations
Santiago Badia, Jesús Bonilla, Juan Vicente Gutiérrez-Santacreu
This paper aims to develop numerical approximations of the Keller--Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. W…
Monotonicity-preserving finite element schemes with adaptive mesh refinement for hyperbolic problems
Jesus Bonilla, Santiago Badia
This work is focused on the extension and assessment of the monotonicity-preserving scheme in [3] and the local bounds preserving scheme in [5] to hierarchical octree adaptive mesh…
On differentiable local bounds preserving stabilization for Euler equations
Santiago Badia, Jesús Bonilla, Sibusiso Mabuza +1
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integr…
Maximum-principle preserving space-time isogeometric analysis
Jesús Bonilla, Santiago Badia
In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The sta…
Differentiable monotonicity-preserving schemes for discontinuous Galerkin methods on arbitrary meshes
Santiago Badia, Jesús Bonilla, Alba Hierro
This work is devoted to the design of interior penalty discontinuous Galerkin (dG) schemes that preserve maximum principles at the discrete level for the steady transport and conve…
Monotonicity-preserving finite element schemes based on differentiable nonlinear stabilization
Santiago Badia, Jesús Bonilla
In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on…