Silvia Bertoluzza

An adaptive collocation method based on interpolating wavelets

A wavelet collocation method for the adaptive solution of second order elliptic partial differential equations in dimension

On the adaptive computation of integrals of wavelets

d

Stable Discretizations of Convection-Diffusion Problems via Computable Negative-Order Inner Products

is presented. The method is based of the use of the Deslaurier-Dubuc interpolating functions. The method is tested on an advection dominated advection diffusion problem, and on a Laplace problem posed on a non rectangular domain. EMAIL:: ian@microian.ian.pv.cnr.it

Analysis of the fully discrete fat boundary method

The numerical solution of partial differential equations involves the computation of integrals of products of given functions and (derivatives of) trial and test functions. We study this problem using adaptively chosen wavelet bases. Firstly, we reduce this problem to the computation of 1-dimensional integrals and present an algorithm for computing these integrals. Then, we consider appropriate adaptive approximations and study the induced error. Finally, we give numerical results.

Wavelet stabilization of the Lagrange multiplier method

A new functional framework for consistently stabilizing discrete approximations to convection-diffusion problems was recently proposed by the authors. The key ideas are the evaluation of the residual in an inner product of the type H-1/2 (unlike classical SUPG methods, which use elemental weighted L2-inner products) and the realization of this inner product via explicitly computable multilevel decompositions of function spaces (such as those given by wavelets or hierarchical finite elements). In this paper, we first provide further motivations for our approach. Next, we carry on a detailed analysis of the method, which covers all regimes (convection-dominated and diffusion-dominated). A consistent part of the analysis justifies the use of easily computable truncated forms of the stabilizing inner product. Numerical results, in close agreement with the theory, are given at the end of the paper.

Analysis of a stabilized three-fields domain decomposition method

The Fat Boundary Method is a method of the Fictitious Domain class, which was proposed to solve elliptic problems in complex geometries with non-conforming meshes. It has been designed to recover optimal convergence at any order, despite of the non-conformity of the mesh, and without any change in the discrete Laplace operator on the simple shape domain. We propose here a detailed proof of this high-order convergence, and propose some numerical tests to illustrate the actual behaviour of the method.

Convergence of a nonlinear wavelet algorithm for the solution of PDEs

Summary. We propose here a stabilization strategy for the Lagrange multiplier formulation of Dirichlet problems. The stabilization is based on the use of equivalent scalar products for the spaces n

The Fat Boundary Method: Semi-Discrete Scheme and Some Numerical Experiments

H^{1/2}(partialOmega)

Negative norm stabilization of convection-diffusion problems☆

and n

Analysis of substructuring preconditioners for mortar methods in an abstract framework

H^{-1/2}(partialOmega)