14 citations · 45 across the 26 of their papers we have counts for
28 papers
Dynamic subscales and unconditional semi-discrete stability for non-residual VMS approximations of generalised Newtonian flows
G. R. Barrenechea, E. Castillo, R. Codina +2
We analyse a non-residual variational multiscale finite element formulation with dynamic subscales for incompressible generalised Newtonian Navier--Stokes flows. The apparent visco…
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 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…
Finite element approximation to linear, second order, parabolic problems with data
Gabriel Barrenechea, Abner J. Salgado
We consider the approximation to the solution of the initial boundary value problem for the heat equation with right hand side and initial condition that merely belong to . Du…
A nodally bound-preserving composite discontinuous Galerkin method on polytopic meshes
Abdolreza Amiri, Gabriel R. Barrenechea, Emmanuil H. Georgoulis +1
We introduce a nodally bound-preserving Galerkin method for second-order elliptic problems on general polygonal/polyhedral, henceforth collectively termed as \emph{polytopic}, mesh…
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 nodally bound-preserving finite element method for time-dependent convection-diffusion equations
Abdolreza Amiri, Gabriel R. Barrenechea, Tristan Pryer
This paper presents a new method to approximate the time-dependent convection-diffusion equations using conforming finite element methods, ensuring that the discrete solution respe…
Unconditionally stable, linearised IMEX schemes for incompressible flows with variable density
Nicolás Espinoza-Contreras, Gabriel Barrenechea, Ernesto Castillo +1
For the incompressible Navier--Stokes system with variable density and viscosity, we propose and analyse an IMEX framework treating the convective and diffusive terms semi-implicit…
A nodally bound-preserving discontinuous Galerkin method for the drift-diffusion equation
Gabriel R. Barrenechea, Tristan Pryer, Alex Trenam
In this work, we introduce and analyse discontinuous Galerkin (dG) methods for the drift-diffusion model. We explore two dG formulations: a classical interior penalty approach and…
A nodally bound-preserving finite element method for reaction-convection-diffusion equations
Abdolreza Amiri, Gabriel R. Barrenechea, Tristan Pryer
This paper introduces a novel approach to approximate a broad range of reaction-convection-diffusion equations using conforming finite element methods while providing a discrete so…
Implicit-explicit schemes for incompressible flow problems with variable viscosity
Gabriel R. Barrenechea, Ernesto Castillo, Douglas R. Q. Pacheco
In this work we study different Implicit-Explicit (IMEX) schemes for incompressible flow problems with variable viscosity. Unlike most previous work on IMEX schemes, which focuses…
A Nodally Bound-Preserving Finite Element Method
Gabriel Barrenechea, Emmanuil Georgoulis, Tristan Pryer +1
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator…
Continuous Interior Penalty stabilization for divergence-free finite element methods
Gabriel R. Barrenechea, Erik Burman, Ernesto Cáceres +1
In this paper we propose, analyze, and test numerically a pressure-robust stabilized finite element for a linearized problem in incompressible fluid mechanics, namely, the steady O…
Finite element methods respecting the discrete maximum principle for convection-diffusion equations
Gabriel R. Barrenechea, Volker John, Petr Knobloch
Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions m…
Analysis of a stabilised finite element method for power-law fluids
Gabriel R. Barrenechea, Endre Suli
A low-order finite element method is constructed and analysed for an incompressible non-Newtonian flow problem with power-law rheology. The method is based on a continuous piecewis…
A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation
Naveed Ahmed, Gabriel R. Barrenechea, Erik Burman +3
Discretization of Navier-Stokes' equations using pressure-robust finite element methods is considered for the high Reynolds number regime. To counter oscillations due to dominating…
Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow
Gabriel Barrenechea, Erik Burman, Johnny Guzmàn
We consider a linearised model of incompressible inviscid flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth d…
Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions
Gabriel R. Barrenechea, Michał Bosy, Victorita Dolean
In several studies it has been observed that, when using stabilised elements for both velocity and pressure, the error for the pressure is sm…
The inf-sup stability of the lowest order Taylor-Hood pair on Anisotropic Meshes
Gabriel R. Barrenechea, Andreas Wachtel
Uniform LBB conditions are desirable to approximate the solution of Navier-Stokes, Oseen, and Stokes equations on anisotropic meshes and to enable anisotropic refinements. We prove…
Numerical assessment of two-level domain decomposition preconditioners for incompressible Stokes and elasticity equations
Gabriel R. Barrenechea, Michał Bosy, Victorita Dolean
Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-le…
Hybrid discontinuous Galerkin discretisation and domain decomposition preconditioners for the Stokes problem
Gabriel R. Barrenechea, Michał Bosy, Victorita Dolean +2
Solving the Stokes equation by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions whose discretisation is not trivia…