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Displaying 201 –
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375
The reduced basis element method is a new approach for approximating
the solution of problems described by partial differential equations.
The method takes its roots in domain decomposition methods and
reduced basis discretizations. The basic idea is to first decompose
the computational domain into a series of subdomains that are deformations
of a few reference domains (or generic computational parts).
Associated with each reference domain are precomputed solutions
corresponding to the same...
This paper is devoted to the introduction of a new variant of the extended
finite element method (Xfem) for the approximation of elastostatic fracture
problems. This variant consists in a reduced basis strategy for the definition
of the crack tip enrichment. It is particularly adapted when the asymptotic
crack-tip displacement is complex or even unknown. We give a mathematical result
of quasi-optimal a priori error estimate and some computational tests including
a comparison with some other strategies....
Subsurface flows are influenced by the presence of faults and large fractures which act as preferential paths or barriers for the flow. In literature models were proposed to handle fractures in a porous medium as objects of codimension 1. In this work we consider the case of a network of intersecting fractures, with the aim of deriving physically consistent and effective interface conditions to impose at the intersection between fractures. This new model accounts for the angle between fractures...
In this paper we develop a residual based a posteriori error analysis for an augmented mixed finite element method applied to the problem of linear elasticity in the plane. More precisely, we derive a reliable and efficient a posteriori error estimator for the case of pure Dirichlet boundary conditions. In addition, several numerical experiments confirming the theoretical properties of the estimator, and illustrating the capability of the corresponding adaptive algorithm to localize the singularities...
In this paper we develop a residual based a posteriori error analysis for an augmented
mixed finite element method applied to the problem of linear elasticity in the plane.
More precisely, we derive a reliable and efficient a posteriori error estimator for the
case of pure Dirichlet boundary conditions. In addition, several numerical
experiments confirming the theoretical properties of the estimator, and
illustrating the capability of the corresponding adaptive algorithm to localize the
singularities...
In 1995, Wahbin presented a method for superconvergence analysis called “Interior symmetric method,” and declared that it is universal. In this paper, we carefully examine two superconvergence techniques used by mathematicians both in China and in America. We conclude that they are essentially different.
In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in -norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.
In this paper, by use of affine biquadratic elements, we construct
and analyze a finite volume element scheme for elliptic equations on
quadrilateral meshes. The scheme is shown to be of second-order in
H1-norm, provided that each quadrilateral in partition is almost
a parallelogram. Numerical experiments are presented to confirm the
usefulness and efficiency of the method.
The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trustregion radius is defined by a Sobolev norm and the trust-region subproblems are solved by a dogleg method. Numerical test results show the method to be effective.
The goal of our paper is to introduce basis functions for the finite element discretization of a second order linear elliptic
operator with rough or highly oscillating coefficients.
The proposed basis functions are inspired by the classic idea of component
mode synthesis and exploit an orthogonal decomposition
of the trial subspace to minimize the energy.
Numerical experiments illustrate the effectiveness of the proposed basis functions.
It is well known that the classical local projection
method as well as residual-based stabilization techniques, as for instance
streamline upwind Petrov-Galerkin (SUPG), are optimal on isotropic
meshes. Here we extend the local projection stabilization for the Navier-Stokes
system to anisotropic quadrilateral meshes in two spatial dimensions. We
describe the new method
and prove an a priori error estimate.
This method leads on anisotropic meshes to qualitatively better
convergence behavior...
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