3 citations · 3 across the 2 of their papers we have counts for
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Nonlinear approximation of high-dimensional anisotropic analytic functions
Diane Guignard, Peter Jantsch
Motivated by nonlinear approximation results for classes of parametric partial differential equations (PDEs), we seek to better understand so-called library approximations to analy…
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…
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…
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…
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…