Diane Sylvie Guignard

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This thesis is devoted to the derivation of error estimates for partial differential equations with random input data, with a focus on a posteriori error estimates which are the basis for adaptive strategies. Such procedures aim at obtaining an approximati ...

We consider finite element error approximations of the steady incompressible Navier-Stokes equations defined on a randomly perturbed domain, the perturbation being small. Introducing a random mapping, these equations are transformed into PDEs on a fixed re ...

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 ...

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 ...

Diane Sylvie Guignard

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A posteriori error estimation for partial differential equations with random input data

A posteriori error estimation for the steady Navier-Stokes equations in random domains

A posteriori error estimations for elliptic partial differential equations with small uncertainties

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method