5 papers · 1 filter
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…
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…
Adaptive Finite Element Methods
Andrea Bonito, Claudio Canuto, Ricardo H. Nochetto +1
This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment i…