10 papers
Analysis and approximation of a two-dimensional induction heating problem
Gabriel R. Barrenechea, Katherine MacKenzie, Abner Salgado
In this paper, we analyse the existence of solutions and finite element approximation of a steady-state two-dimensional induction heating problem. One of the main difficulties of t…
An Aubin-Nitsche Lemma for a positivity-preserving finite element method
Gabriel R. Barrenechea, Theophile Chaumont-Frelet
In this work we prove an Aubin-Nitsche Lemma for a positivity-preserving discretisation of an elliptic problem. Due to the nonlinearity of the discretisation, the result requires a…
A stabilized finite element method for a flow problem arising from 4D flow magnetic resonance imaging
Gabriel Barrenechea, Cristian Cárcamo, Abner Poza
In this work we propose, {analyze}, and validate a stabilized finite element method for a flow problem arising from the assessment of {4D Flow Magnetic Resonance Imaging quality}.…
A finite element method preserving the eigenvalue range of symmetric tensor fields
Abdolreza Amiri, Gabriel R. Barrenechea, Tristan Pryer
This paper presents a finite element method that preserves (at the degrees of freedom) the eigenvalue range of the solution of tensor-valued time-dependent convection--diffusion eq…
A bound-preserving and conservative enriched Galerkin method for elliptic problems
Gabriel R. Barrenechea, Philip L. Lederer, Andreas Rupp
We propose a locally conservative enriched Galerkin scheme that preserves the physical bounds for an elliptic problem. To this end, we use a substantial over-penalization of the di…
A finite element method for a non-Newtonian dilute polymer fluid
Ben S. Ashby, Gabriel R. Barrenechea, Alex Lukyanov +2
We study the discretisation of a uniaxial (rank-one) reduction of the Oldroyd-B model for dilute polymer solutions, in which the conformation tensor is represented as $\sig = \vec…