In this paper we construct a new H(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
(div, ), which is closely related to the energy...
In this paper we construct a new (div)-conforming projection-based
-interpolation operator that assumes only
()
(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
(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,...
We analyse a finite-element discretisation of a differential equation describing an axisymmetrically loaded thin shell. The problem is singularly perturbed when the thickness of the shell becomes small. We prove robust convergence of the method in a balanced norm that captures the layers present in the solution. Numerical results confirm our findings.
A model two-dimensional acoustic waveguide with lateral impedance boundary conditions (and outgoing boundary conditions at the waveguide outlet) is considered. The governing operator is proved to be bounded below with a stability constant inversely proportional to the length of the waveguide. The presence of impedance boundary conditions leads to a non self-adjoint operator which considerably complicates the analysis. The goal of this paper is to elucidate these complications and tools that are...
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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