7 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: 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…
-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…