An adaptive algorithm for the Stokes problem using continuous, piecewise linear stabilized finite elements and meshes with high aspect ratio
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In this work, we consider an elliptic partial differential equation (PDE) with a random coefficient solved with the stochastic collocation finite element method (SC-FEM). The random diffusion coefficient is assumed to depend in an affine way on independent ...
In this work, we consider an elliptic partial differential equation with a random coefficient solved with the stochastic collocation finite element method. The random diffusion coefficient is assumed to depend in an affine way on independent random variabl ...
In this article, a finite element error analysis is performed on a class of linear and nonlinear elliptic problems with small uncertain input. Using a perturbation approach, the exact (random) solution is expanded up to a certain order with respect to a pa ...
We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance ...
We consider goal-oriented a posteriori error estimators for the evaluation of the errors on quantities of interest associated with the solution of geometrically nonlinear curved elastic rods. For the numerical solution of these nonlinear one-dimensional pr ...
Engineers rely on efficient simulations that provide them with reliable data in order to make proper engineering design decisions. The purpose of this thesis is to design adaptive numerical methods for multiscale problems in this spirit. We consider ellipt ...
A reduced basis finite element heterogeneous multiscale method (RB-FE-HMM) for a class of nonlinear homogenization elliptic problems of nonmonotone type is introduced. In this approach, the solutions of the micro problems needed to estimate the macroscopic ...
We consider the numerical approximation of the stochastic Darcy problem with log-normal permeability field and propose a novel Multi Level Monte Carlo (MLMC) approach with a control variate variance reduction technique on each level. We model the log-perme ...
We consider the numerical approximation of the stochastic Darcy problem with log-normal permeability field and propose a novel Multi Level Monte Carlo approach with a control variate variance reduction technique on each level. We model the log-permeability ...
We present an "a posteriori" error analysis in quantities of interest for elliptic homogenization problems discretized by the finite element heterogeneous multiscale method. The multiscale method is based on a macro-to-micro formulation, where the macrosco ...