145 citations · 609 across the 61 of their papers we have counts for
78 papers
Virtual element methods for a class of fully nonlinear elliptic PDEs
Guillaume Bonnet, Andrea Cangiani, Andreas Dedner +1
We study virtual element discretizations of a well-known variational formulation in of Hamilton-Jacobi-Bellman and Isaacs equations with Cordes coefficients. We show that the…
Existence of weak solutions of the surface Beris-Edwards model
Gonzalo A. Benavides, Ricardo H. Nochetto, Mansur Shakipov
We prove the existence of weak solutions to the surface Beris-Edwards model for nematic liquid crystals posed on a -dimensional () closed hypersurface of class $C…
A Virtual Element Method for elliptic problems on trimmed background meshes
L. Beirão da Veiga, C. Canuto, R. H. Nochetto +2
We consider a two-dimensional piecewise domain that cuts through a quasi-uniform fixed polygonal background mesh, for instance made of quadrilaterals. A simple procedure base…
Ferrofluids: Modeling and Approximation
Gonzalo A. Benavides, Ricardo H. Nochetto, Mansur Shakipov
Starting from Maxwell's and linear momentum balance equations, we derive a ferrofluid model using the generalized Onsager's principle. Guided by a discrete perturbation estimate, w…
-based Sobolev theory on closed manifolds of minimal regularity: Scalar Elliptic Equations
Gonzalo A. Benavides, Ricardo H. Nochetto, Mansur Shakipov
This paper and its follow-up arXiv:2508.11109 are concerned with the well-posedness and -based Sobolev regularity for appropriate weak formulations of a family of pro…
Surface Stokes Without Inf-Sup Condition
Ricardo H. Nochetto, Mansur Shakipov
For a -dimensional hypersurface of class without boundary, we reformulate the surface Stokes equations as a nonsymmetric indefinite elliptic problem governed by two Laplac…
-based Sobolev theory on closed manifolds of minimal regularity: Vector-valued problems
Gonzalo A. Benavides, Ricardo H. Nochetto, Mansur Shakipov
This paper is the second part of a two-paper series, initiated in arXiv:2603.02163 for scalar PDEs on hypersurfaces, and is concerned with the well-posedness and -bas…
Inf-Sup Stability of Parabolic TraceFEM
Lucas Bouck, Ricardo H. Nochetto, Mansur Shakipov +1
We develop a parabolic inf-sup theory for a modified TraceFEM semi-discretization in space of the heat equation posed on a stationary surface embedded in . We conside…
Projection-Free Method for the Full Frank-Oseen Model of Liquid Crystals
Lucas Bouck, Ricardo H. Nochetto
Liquid crystals are materials that experience an intermediate phase where the material can flow like a liquid, but the molecules maintain an orientation order. The Frank-Oseen mode…
Monotone two-scale methods for a class of integrodifferential operators and applications
Juan Pablo Borthagaray, Ricardo H. Nochetto, Abner J. Salgado +1
We develop a monotone, two-scale discretization for a class of integrodifferential operators of order , . We apply it to develop numerical schemes, and derive poin…
Conforming virtual element method for nondivergence form linear elliptic equations with Cordes coefficients
Guillaume Bonnet, Andrea Cangiani, Ricardo H. Nochetto
We propose and analyze an -conforming Virtual Element Method (VEM) for the simplest linear elliptic PDEs in nondivergence form with Cordes coefficients. The VEM hinges on a hi…
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…
Quasi-linear fractional-order operators in Lipschitz domains
Juan Pablo Borthagaray, Wenbo Li, Ricardo H. Nochetto
We prove Besov boundary regularity for solutions of the homogeneous Dirichlet problem for fractional-order quasi-linear operators with variable coefficients on Lipschitz domains $Ω…
Adaptive VEM for variable data: convergence and optimality
L. Beirão da Veiga, C. Canuto, R. H. Nochetto +2
We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization…
-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…
Fractional Elliptic Problems on Lipschitz Domains: Regularity and Approximation
Juan Pablo Borthagaray, Wenbo Li, Ricardo H. Nochetto
This survey hinges on the interplay between regularity and approximation for linear and quasi-linear fractional elliptic problems on Lipschitz domains. For the linear Dirichlet int…
Reduced Membrane Model for Liquid Crystal Polymer Networks: Asymptotics and Computation
Lucas Bouck, Ricardo H. Nochetto, Shuo Yang
We examine a reduced membrane model of liquid crystal polymer networks (LCNs) via asymptotics and computation. This model requires solving a minimization problem for a non-convex s…
Convergent FEM for a membrane model of liquid crystal polymer networks
Lucas Bouck, Ricardo H. Nochetto, Shuo Yang
We design a finite element method (FEM) for a membrane model of liquid crystal polymer networks (LCNs). This model consists of a minimization problem of a non-convex stretching ene…
A hydrodynamical model of nematic liquid crystal films with a general state of orientational order
Lucas Bouck, Ricardo H. Nochetto, Vladimir Yushutin
We develop a Q-tensor model of nematic liquid crystals occupying a stationary surface which represents a fluidic material film in space. In addition to the evolution due to Landau-…
Besov regularity for the Dirichlet integral fractional Laplacian in Lipschitz domains
Juan Pablo Borthagaray, Ricardo H. Nochetto
We prove Besov regularity estimates for the solution of the Dirichlet problem involving the integral fractional Laplacian of order in bounded Lipschitz domains : \[ \begin{a…
Constructive approximation on graded meshes for the integral fractional Laplacian
Juan Pablo Borthagaray, Ricardo H. Nochetto
We consider the homogeneous Dirichlet problem for the integral fractional Laplacian . We prove optimal Sobolev regularity estimates in Lipschitz domains provided the soluti…
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 algorithms for nonlocal minimal graphs
Juan Pablo Borthagaray, Wenbo Li, Ricardo H. Nochetto
We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a…
Gamma-convergent projection-free finite element methods for nematic liquid crystals: The Ericksen model
Ricardo H. Nochetto, Michele Ruggeri, Shuo Yang
The Ericksen model for nematic liquid crystals couples a director field with a scalar degree of orientation variable, and allows the formation of various defects with finite energy…