145 citations · 609 across the 61 of their papers we have counts for
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The Stokes problem with Navier slip boundary condition: Minimal fractional Sobolev regularity of the domain
Harbir Antil, Ricardo H. Nochetto, Patrick Sodre
We prove well-posedness in reflexive Sobolev spaces of weak solutions to the stationary Stokes problem with Navier slip boundary condition over bounded domains of $\mathbb{R}^n…
The equations of ferrohydrodynamics: modeling and numerical methods
Ricardo H. Nochetto, Abner J. Salgado, Ignacio Tomas
We discuss the equations describing the motion of ferrofluids subject to an external magnetic field. We concentrate on the model proposed by R. Rosensweig, provide an appropriate d…
Fast multilevel solvers for a class of discrete fourth order parabolic problems
Bin Zheng, Luoping Chen, Xiaozhe Hu +3
In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass m…
High-Order AFEM for the Laplace-Beltrami Operator: Convergence Rates
Andrea Bonito, J. Manuel Cascón, Pedro Morin +2
We present a new AFEM for the Laplace-Beltrami operator with arbitrary polynomial degree on parametric surfaces, which are globally and piecewise in a suitable Besov c…
Adaptive Spectral Galerkin Methods with Dynamic Marking
Claudio Canuto, Ricardo H. Nochetto, Rob Stevenson +1
The convergence and optimality theory of adaptive Galerkin methods is almost exclusively based on the Dörfler marking. This entails a fixed parameter and leads to a contraction con…
A PDE Approach to Numerical Fractional Diffusion
Ricardo H. Nochetto, Enrique Otarola, Abner J. Salgado
Fractional diffusion has become a fundamental tool for the modeling of multiscale and heterogeneous phenomena. However, due to its nonlocal nature, its accurate numerical approxima…
Convergence and Optimality of hp-AFEM
Claudio Canuto, Ricardo H. Nochetto, Rob Stevenson +1
We design and analyze an adaptive -finite element method (hp-AFEM) in dimensions . The algorithm consists of iterating two routines: hp-NEARBEST finds a near-best -a…