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In this paper we address the numerical approximation of the incompressible Navier-Stokes equations in a moving domain by the spectral element method and high order time integrators. We present the Arbitrary Lagrangian Eulerian (ALE) formulation of the inco ...
The goals of this project are to study and numerically solve a reduced fluid-structure interaction problem for cardiovascular applications. The first section of this project presents two test cases in order to understand the finite element method for two d ...
An analysis of a multiscale symmetric interior penalty discontinuous Galerkin finite element method for the numerical discretization of elliptic problems with multiple scales is proposed. This new method, first described in [A. Abdulle, C.R. Acad. Sci. Par ...
In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by mu ...
Solving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numeri ...
We consider the fluid-structure interaction problem arising in haemodynamic applications. The finite elasticity equations for the vessel are written in Lagrangian form, while the Navier-Stokes equations for the blood in Arbitrary Lagrangian Eulerian form. ...
Numerical methods for parabolic homogenization problems combining finite element methods (FEMs) in space with Runge-Kutta methods in time are proposed. The space discretization is based on the coupling of macro and micro finite element methods following th ...
In this paper we propose a reduced basis hybrid method (RBHM) for the approximation of partial differential equations in domains represented by complex networks where topological features are recurrent. The RBHM is applied to Stokes equations in domains wh ...
A large portion of software is used for numerical calculations in mathematics, physics and engineering applications. Among the things that make verification in this domain difficult is the quantification of numerical errors, such as roundoff errors and err ...
The objective of this work is to develop a numerical framework to perform rapid and reliable simulations for solving parametric problems in domains represented by networks and to extend the classical reduced basis method. Aimed at this scope, we propose tw ...
