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A new H(div)-conforming p-interpolation operator in two dimensions

Alexei BespalovNorbert Heuer — 2011

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we construct a new H(div)-conforming projection-based -interpolation operator that assumes only H() 𝐇 ˜ (div, )-regularity ( > 0) on the reference element (either triangle or square) . We show that this operator is stable with respect to polynomial degrees and satisfies the commuting diagram property. We also establish an estimate for the interpolation error in the norm of the space 𝐇 ˜ (div, ), which is closely related to the energy...

A new (div)-conforming -interpolation operator in two dimensions

Alexei BespalovNorbert Heuer — 2011

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we construct a new (div)-conforming projection-based -interpolation operator that assumes only () 𝐇 ˜ (div, )-regularity ( > 0) on the reference element (either triangle or square) . We show that this operator is stable with respect to polynomial degrees and satisfies the commuting diagram property. We also establish an estimate for the interpolation error in the norm of the space 𝐇 ˜ (div, ), which is closely related to...

The -version of the boundary element method with quasi-uniform meshes in three dimensions

Alexei BespalovNorbert Heuer — 2008

ESAIM: Mathematical Modelling and Numerical Analysis

We prove an error estimate for the -version of the boundary element method with hypersingular operators on piecewise plane open or closed surfaces. The underlying meshes are supposed to be quasi-uniform. The solutions of problems on polyhedral or piecewise plane open surfaces exhibit typical singularities which limit the convergence rate of the boundary element method. On closed surfaces, and for sufficiently smooth given data, the solution is -regular whereas, on open surfaces,...

A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity

Tomás P. BarriosGabriel N. GaticaMaría GonzálezNorbert Heuer — 2006

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

A residual based error estimator for an augmented mixed finite element method in linear elasticity

Tomás P. BarriosGabriel N. GaticaMaría GonzálezNorbert Heuer — 2007

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we develop a residual based 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 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 and the large stress...

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