5 papers
Splitting-strategies for arbitrary-order fully mixed finite element discretizations of the Biot equations
Fleurianne Bertrand, Jakub Wiktor Both, Tugay DaÄlı +1
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 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…
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…
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…
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…