152 citations · 839 across the 37 of their papers we have counts for
5 papers · 2 filters
Stability and conditioning of immersed finite element methods: analysis and remedies
Frits de Prenter, Clemens Verhoosel, Harald van Brummelen +2
This review paper discusses the developments in immersed or unfitted finite element methods over the past decade. The main focus is the analysis and the treatment of the adverse ef…
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…
Space-time unfitted finite element methods for time-dependent problems on moving domains
Santiago Badia, Hridya Dilip, Francesc Verdugo
We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation o…
A comparison of variational upwinding schemes for geophysical fluids, and their application to potential enstrophy conserving discretisations
David Lee, Alberto F. Martín, Christopher Bladwell +1
Methods for upwinding the potential vorticity in a compatible finite element discretisation of the rotating shallow water equations are studied. These include the well-known antici…
Robust high-order unfitted finite elements by interpolation-based discrete extension
Santiago Badia, Eric Neiva, Francesc Verdugo
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on…