In this paper we construct a new H(div)-conforming projection-based -interpolation operator that assumes only H() $\cap $
$\tilde{\mathbf{H}}$
(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 $\tilde{\mathbf{H}}$
(div, ), which is closely related to the energy...

In this paper we construct a new (div)-conforming projection-based
-interpolation operator that assumes only
() $\cap $
$\tilde{\mathbf{H}}$
(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 $\tilde{\mathbf{H}}$
(div, ),
which is closely related to...

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,...

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 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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