7 papers · 1 filter
A near-optimal recovery algorithm for the Stokes equations with incomplete information on the boundary conditions
Andrea Bonito, Diane Guignard
We address the problem of numerically approximating the velocity and pressure governed by the Stokes system when the boundary conditions are only partially known and thus do not un…
Error analysis for the approximation of a flow in deformable porous media with nonlinear strain-stress relation
Andrea Bonito, Vivette Girault, Diane Guignard
We study a model describing the slow flow of a fluid through a deformable, porous, elastic solid undergoing small deformations. The stress-strain relationship of the solid incorpor…
Convergence analysis for a tree-based nonlinear reduced basis method
Mohamed Barakat, Diane Guignard
We develop and analyze a nonlinear reduced basis (RB) method for parametrized elliptic partial differential equations based on a binary-tree partition of the parameter domain into…
Finite Element Methods for the Stretching and Bending of Thin Structures with Folding
Andrea Bonito, Diane Guignard, Angelique Morvant
In [Bonito et al., J. Comput. Phys. (2022)], a local discontinuous Galerkin method was proposed for approximating the large bending of prestrained plates, and in [Bonito et al., IM…
Approximating partial differential equations without boundary conditions
Andrea Bonito, Diane Guignard
We consider the problem of numerically approximating the solutions to an elliptic partial differential equation (PDE) for which the boundary conditions are lacking. To alleviate th…
Numerical Approximation of Gaussian random fields on Closed Surfaces
Andrea Bonito, Diane Guignard, Wenyu Lei
We consider the numerical approximation of Gaussian random fields on closed surfaces defined as the solution to a fractional stochastic partial differential equation (SPDE) with ad…