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An adaptive Uzawa FEM for the Stokes problem: Convergence without the inf-sup condition
(Society for Industrial and Applied Mathematics, 2002-09)
We introduce and study an adaptive finite element method (FEM) for the Stokes system based on an Uzawa outer iteration to update the pressure and an elliptic adaptive inner iteration for velocity. We show linear convergence ...
Convergence of Adaptive Finite Element Methods
(Society for Industrial and Applied Mathematics, 2002-12)
Adaptive finite element methods (FEMs) have been widely used in applications for over 20 years now. In practice, they converge starting from coarse grids, although no mathematical theory has been able to prove this assertion. ...
Proceso automatizado de refinamiento H-adaptativo usando índices de energía de deformación
(Ciencia e Ingeniería, 2010)
Adaptive finite element method for shape optimization
(Cambridge University Press, 2012-10)
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations ...
Application of PHT-splines in bending and vibration analysis of cracked Kirchhoff-Love plates
(Elsevier, 2020)
In this work, we present an eXtended Geometry Independent Field approximaTion (X-GIFT) formulation for cracked Kirchhoff-Love plates. The plate geometry is modeled by Non-Uniform Rational B-Splines (NURBS) while the solution ...
A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation
(GLOBAL SCIENCE PRESS, 2010)
We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid ...
Adaptive Simulation of the Internal Flow in a Rocket Nozzle
(Planta Piloto de Ingeniería Química, 2014-07)
This work is a first step in the understanding of the interaction process between internal shock waves and the flow transition inside of a rocket nozzle that develops during the engine start-up phase or when the nozzle is ...