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Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces in case of hexahedral triangulations. As a result, standard efficient iterative solvers as...
Domain decomposition techniques provide a flexible tool for the numerical
approximation of partial differential equations. Here, we consider
mortar techniques for quadratic finite elements in 3D with
different Lagrange multiplier spaces.
In particular, we
focus on Lagrange multiplier spaces
which yield optimal discretization
schemes and a locally supported basis for the associated
constrained mortar spaces in case
of hexahedral triangulations. As a result,
standard efficient iterative solvers...
A new postprocessing technique suitable for nonuniform triangulations is employed in the sensitivity analysis of some model optimal shape design problems.
A recovery-based a posteriori error estimator for the generalized Stokes problem is established based on the stabilized (linear/constant) finite element method. The reliability and efficiency of the error estimator are shown. Through theoretical analysis and numerical tests, it is revealed that the estimator is useful and efficient for the generalized Stokes problem.
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.
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