13 citations · 31 across the 26 of their papers we have counts for
31 papers
Splitting-strategies for arbitrary-order fully mixed finite element discretizations of the Biot equations
Fleurianne Bertrand, Jakub Wiktor Both, Tugay Dağlı
We study the fully-mixed formulation of the Biot equations which is characterized by a symmetric coupling between flow and deformation while each subphysics has internally a saddle…
Least squares spectral element formulation of eigenvalue problems with/without interface : the one dimensional example
Himanshu Garg, Fleurianne Bertrand, Subhashree Mohapatra
Here, we present a least-squares based spectral element formulation for one-dimensional eigenvalue problems with interface conditions. First we develop the method for without inter…
Least-Squares Finite Element Methods for nonlinear problems: A unified framework
Fleurianne Bertrand, Maximilian Brodbeck, Tim Ricken +1
This paper presents a unified Least-Squares framework for solving nonlinear partial differential equations by recasting the governing system as a residual minimisation problem. A L…
Adaptive finite element methods based on flux and stress equilibration using FEniCSx
Maximilian Brodbeck, Fleurianne Bertrand, Tim Ricken
This contribution shows how a-posteriori error estimators based on equilibrated fluxes - H(div) functions fulfilling the underlying conservation law - can be implemented in FEniCSx…
A variant of the Raviart-Thomas method to handle smooth domains using straight-edged triangles. Part II -- Approximation results
Fleurianne Bertrand, Vitoriano Ruas
In arXiv:2307.03503 [math.NA] we commenced to study a variant of the Raviart-Thomas mixed finite element method for triangles, to solve second order elliptic equations in a curved…
A variant of the Raviart-Thomas method for smooth domains with straight-edged triangles
Fleurianne Bertrand, Vitoriano Ruas
Several physical problems modeled by second-order elliptic equations can be efficiently solved using mixed finite elements of the Raviart-Thomas family RTk for N-simplexes, introdu…
Least-Squares finite element method for the simulation of sea-ice motion
Fleurianne Bertrand, Henrik Schneider
A nonlinear sea-ice problem is considered in a least-squares finite element setting. The corresponding variational formulation approximating simultaneously the stress tensor and th…
Approximation of the Maxwell eigenvalue problem in a Least-Squares setting
Fleurianne Bertrand, Daniele Boffi, Lucia Gastaldi
We discuss the approximation of the eigensolutions associated with the Maxwell eigenvalues problem in the framework of least-squares finite elements. We write the Maxwell curl curl…
A data-driven method for parametric PDE Eigenvalue Problems using Gaussian Process with different covariance functions
Moataz Alghamdi, Fleurianne Bertrand, Daniele Boffi +1
We use a Gaussian Process Regression (GPR) strategy that was recently developed [3,16,17] to analyze different types of curves that are commonly encountered in parametric eigenvalu…
Contact problems in porous media
L. Banz, F. Bertrand
The Biot problem of poroelasticity is extended by Signorini contact conditions. The resulting Biot contact problem is formulated and analyzed as a two field variational inequality…
Data-driven reduced order modeling for parametric PDE eigenvalue problems using Gaussian process regression
Fleurianne Bertrand, Daniele Boffi, Abdul Halim
In this article, we propose a data-driven reduced basis (RB) method for the approximation of parametric eigenvalue problems. The method is based on the offline and online paradigms…
Superconvergence of discontinuous Petrov-Galerkin approximations in linear elasticity
Fleurianne Bertrand, Henrik Schneider
Existing a priori convergence results of the discontinuous Petrov-Galerkin method to solve the problem of linear elasticity are improved. Using duality arguments, we show that high…
On the matching of eigensolutions to parametric partial differential equations
Moataz M. Alghamdi, Fleurianne Bertrand, Daniele Boffi +3
In this paper a novel numerical approximation of parametric eigenvalue problems is presented. We motivate our study with the analysis of a POD reduced order model for a simple one…
Stabilization-free HHO a posteriori error control
Fleurianne Bertrand, Carsten Carstensen, Benedikt Gräßle +1
The known a posteriori error analysis of hybrid high-order methods (HHO) treats the stabilization contribution as part of the error and as part of the error estimator for an effici…
On the necessity of the inf-sup condition for a mixed finite element formulation
Fleurianne Bertrand, Daniele Boffi
We study a non standard mixed formulation of the Poisson problem, sometimes known as dual mixed formulation. For reasons related to the equilibration of the flux, we use finite ele…
A reduced order model for the finite element approximation of eigenvalue problems
Fleurianne Bertrand, Daniele Boffi, Abdul Halim
In this paper we consider a reduced order method for the approximation of the eigensolutions of the Laplace problem with Dirichlet boundary condition. We use a time continuation te…
A phase-space discontinuous Galerkin approximation for the radiative transfer equation in slab geometry
Riccardo Bardin, Fleurianne Bertrand, Olena Palii +1
We derive and analyze a symmetric interior penalty discontinuous Galerkin scheme for the approximation of the second-order form of the radiative transfer equation in slab geometry.…
On the spectrum of an operator associated with least-squares finite elements for linear elasticity
Linda Alzaben, Fleurianne Bertrand, Daniele Boffi
In this paper we provide some more details on the numerical analysis and we present some enlightening numerical results related to the spectrum of a finite element least-squares ap…
DPG approximation of eigenvalue problems
Fleurianne Bertrand, Daniele Boffi, Henrik Schneider
In this paper, the discontinuous Petrov--Galerkin approximation of the Laplace eigenvalue problem is discussed. We consider in particular the primal and ultra weak formulations of…
A posteriori error estimates by weakly symmetric stress reconstruction for the Biot problem
F. Bertrand, G. Starke
A posteriori error estimates are constructed for the three-field variational formulation of the Biot problem involving the displacements, the total pressure and the fluid pressure.…
Least Squares Finite Element Method for Hepatic Sinusoidal Blood Flow
Fleurianne Bertrand, Lena Lambers, Tim Ricken
The simulation of complex biological systems such as the description of blood flow in organs requires a lot of computational power as well as a detailed description of the organ ph…
Convergence analysis of the scaled boundary finite element method for the Laplace equation
Fleurianne Bertrand, Daniele Boffi, Gonzalo G. de Diego
The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamenta…
An adaptive finite element scheme for the Hellinger--Reissner elasticity mixed eigenvalue problem
Fleurianne Bertrand, Daniele Boffi, Rui Ma
In this paper we study the approximation of eigenvalues arising from the mixed Hellinger--Reissner elasticity problem by using the simple finite element using partial relaxation of…
Least-squares for linear elasticity eigenvalue problem
Fleurianne Bertrand, Daniele Boffi
We study the approximation of the spectrum of least-squares operators arising from linear elasticity. We consider a two-field (stress/displacement) and a three-field (stress/displa…