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- J. Donea, Antonio Huerta, A. Rodrı́guez-Ferran
- 2004

The numerical simulation of multidimensional problems in fluid dynamics and nonlinear solid mechanics often requires coping with strong distortions of the continuum under consideration while allowing for a clear delineation of free surfaces and fluid–fluid, solid–solid, or fluid–structure interfaces. A fundamentally important consideration when developing a… (More)

A new residual-type flux-free error estimator is presented. It computes upper and lower bounds of the error in energy norm with the ultimate goal of obtaining bounds for outputs of interest. The proposed approach precludes the main drawbacks of standard residual type estimators circumventing the need of flux-equilibration and resulting in a simple… (More)

We present a method for the computation of upper and lower bounds for linear-functional outputs of the exact solutions to the two dimensional elasticity equations. The method can be regarded as a generalization of the well known complementary energy principle. The desired output is cast as the supremum of a linear-quadratic convex functional over an… (More)

- A. M. Sauer-Budge, Javier Bonet, Antonio Huerta, Jaime Peraire
- SIAM J. Numerical Analysis
- 2004

We present a method for Poisson’s equation that computes guaranteed upper and lower bounds for the values of linear functional outputs of the exact weak solution of the infinite dimensional continuum problem using traditional finite element approximations. The guarantee holds uniformly for any level of refinement, not just in the asymptotic limit of… (More)

We discuss, in this paper, a flux-free method for the computation of strict upper bounds of the energy norm of the error in a Finite Element (FE) computation. The bounds are strict in the sense that they refer to the difference between the displacement computed on the FE mesh and the exact displacement, solution of the continuous equations, rather than to… (More)

- Eva Casoni, Antonio Huerta
- 2009

Abstract. This work is devoted to solve scalar hyperbolic conservation laws in the presence of strong shocks with discontinuous Galerkin methods (DGM). A standard approach is to use limiting strategies in order to avoid oscillations in the vicinity of the shock. Basically, these techniques reconstruct the solution with a lower order polynomial in those… (More)

A Discontinuous Galerkin (DG) method with solenoidal approximation for the simulation of incompressible flow is proposed. It is applied to the solution of the Stokes equations. The Interior Penalty Method is employed to construct the DG weak form. For every element, the approximation space for the velocity field is decomposed as direct sum of a solenoidal… (More)

Abstract. The spatial discretization of the unsteady incompressible Navier-Stokes equations is stated as a system of Differential Algebraic Equations (DAEs), corresponding to the conservation of momentum equation plus the constraint due to the incompressibility condition. Runge-Kutta methods applied to the solution of the resulting index-2 DAE system are… (More)

- Jose Vicente Aguado, Francisco Chinesta, +7 authors Antonio Huerta
- 2013

Abstract. A new technique for efficiently solving parametric nonlinear reduced order models in the Proper Generalized Decomposition (PGD) framework is presented here. This technique is based on the Discrete Empirical Interpolation Method (DEIM)[1], and thus the nonlinear term is interpolated using the reduced basis instead of being fully evaluated. The DEIM… (More)

- AgustmH PeH, rez-Foguet, Antonio RodrmHguez-Ferran, Antonio Huerta
- 2001

The consistent tangent matrix for density-dependent plastic models within the theory of isotropic multiplicative hyperelastoplasticity is presented here. Plastic equations expressed as general functions of the Kirchho! stresses and density are considered. They include the Cauchy-based plastic models as a particular case. The standard exponential… (More)