145 citations · 289 across the 31 of their papers we have counts for
44 papers
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…
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…
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…
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…
Solving PDEs with Incomplete Information
Peter Binev, Andrea Bonito, Albert Cohen +3
We consider the problem of numerically approximating the solutions to a partial differential equation (PDE) when there is insufficient information to determine a unique solution. O…
-convergent LDG method for large bending deformations of bilayer plates
Andrea Bonito, Ricardo H. Nochetto, Shuo Yang
Bilayer plates are slender structures made of two thin layers of different materials. They react to environmental stimuli and undergo large bending deformations with relatively sma…
Numerical approximations of thin structure deformations
Andrea Bonito, Diane Guignard, Angelique Morvant
We review different (reduced) models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists in the minimization of a fourth ord…
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…
Error Estimates For A Linear Folding Model
Sören Bartels, Andrea Bonito, Philipp Tscherner
An interior penalty discontinuous Galerkin method is devised to approximate minimizers of a linear folding model by discontinuous isoparametric finite element functions that accoun…
Optimal Learning
Peter Binev, Andrea Bonito, Ronald DeVore +1
This paper studies the problem of learning an unknown function from given data about . The learning problem is to give an approximation to that predicts the val…
Modeling and simulation of thin sheet folding
Sören Bartels, Andrea Bonito, Peter Hornung
The article addresses the mathematical modeling of the folding of a thin elastic sheet along a prescribed curved arc. A rigorous model reduction from a general hyperelastic materia…
Numerical analysis of the LDG method for large deformations of prestrained plates
Andrea Bonito, Diane Guignard, Ricardo Nochetto +1
A local discontinuous Galerkin (LDG) method for approximating large deformations of prestrained plates is introduced and tested on several insightful numerical examples in our prev…
Finite Element Approximation of Steady Flows of Colloidal Solutions
Andrea Bonito, Vivette Girault, Diane Guignard +2
We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isocho…
Approximation of the spectral fractional powers of the Laplace-Beltrami Operator
Andrea Bonito, Wenyu Lei
We consider numerical approximations of spectral fractional Laplace-Beltrami problems on closed surfaces. The proposed numerical algorithms rely on their Balakrishnan integral repr…
LDG approximation of large deformations of prestrained plates
Andrea Bonito, Diane Guignard, Ricardo H. Nochetto +1
A reduced model for large deformations of prestrained plates consists of minimizing a second order bending energy subject to a nonconvex metric constraint. The former involves the…
Numerical Simulations of Surface-Quasi Geostrophic Flows on Periodic Domains
Andrea Bonito, Murtazo Nazarov
We propose a novel algorithm for the approximation of surface-quasi geostrophic (SQG) flows modeled by a nonlinear partial differential equation coupling transport and fractional d…
Nonlinear Methods for Model Reduction
Andrea Bonito, Albert Cohen, Ronald DeVore +3
The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space which approximates well the solution manifold $\math…
Discontinuous Galerkin Approach to Large Bending Deformation of a Bilayer Plate with Isometry Constraint
Andrea Bonito, Ricardo H. Nochetto, Dimitris Ntogkas
We present a computational model of thin elastic bilayers that undergo large bending isometric deformations when actuated by non-mechanical stimuli. We propose a discontinuous Gale…
DG Approach to Large Bending Plate Deformations with Isometry Constraint
Andrea Bonito, Ricardo H. Nochetto, Dimitrios Ntogkas
We propose a new discontinuous Galerkin (dG) method for a geometrically nonlinear Kirchhoff plate model for large isometric bending deformations. The minimization problem is noncon…
A divergence-conforming finite element method for the surface Stokes equation
Andrea Bonito, Alan Demlow, Martin Licht
The Stokes equation posed on surfaces is important in some physical models, but its numerical solution poses several challenges not encountered in the corresponding Euclidean setti…
Finite Element Methods for the Laplace-Beltrami Operator
Andrea Bonito, Alan Demlow, Ricardo H. Nochetto
Partial differential equations posed on surfaces arise in a number of applications. In this survey we describe three popular finite element methods for approximating solutions to t…
Reduced Basis Approximations of the Solutions to Spectral Fractional Diffusion Problems
Andrea Bonito, Diane Guignard, Ashley R. Zhang
We consider the numerical approximation of the spectral fractional diffusion problem based on the so called Balakrishnan representation. The latter consists of an improper integral…
Polynomial Approximation of Anisotropic Analytic Functions of Several Variables
Andrea Bonito, Ronald DeVore, Diane Guignard +2
Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomia…
Electroconvection of Thin Liquid Crystals: Model Reduction and Numerical Simulations
Andrea Bonito, Peng Wei
We propose a finite element method for the numerical simulation of electroconvection of thin liquid crystals. The liquid is located in between two concentric circular electrodes wh…