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We analyze a numerical model for the Signorini unilateral contact, based on the mortar method, in the quadratic finite element context. The mortar frame enables one to use non-matching grids and brings facilities in the mesh generation of different components of a complex system. The convergence rates we state here are similar to those already obtained for the Signorini problem when discretized on conforming meshes. The matching for the unilateral contact driven by mortars preserves then the proper...
In this paper, we prove that integral -varifolds in codimension 1 with , , have quadratic tilt-excess decay for -almost all , and a strong maximum principle which states that these varifolds cannot be touched by smooth manifolds whose mean curvature is given by the weak mean curvature , unless the smooth manifold is locally contained in the support of .
We estimate the spreading of the solution of the Schrödinger equation asymptotically in time, in term of the fractal properties of the associated spectral measures. For this, we exhibit a lower bound for the moments of order at time for the state defined by . We show that this lower bound can be expressed in term of the generalized Rényi dimension of the spectral measure associated to the hamiltonian and the state . We especially concentrate on continuous models.
A quasiharmonic field is a pair of vector fields satisfying , , and coupled by a distorsion inequality. For a given , we construct a matrix field such that . This remark in particular shows that the theory of quasiharmonic fields is equivalent (at least locally) to that of elliptic PDEs. Here we stress some properties of our operator and find their applications to the study of regularity of solutions to elliptic PDEs, and to some questions of G-convergence.
One of the main tools in the proof of residual-based a posteriori error
estimates is a quasi-interpolation operator due to Clément.
We modify this operator in the setting of a partition of unity
with the effect that the approximation error has a local average zero.
This results in a new residual-based a posteriori error estimate
with a volume contribution which is smaller than in the standard estimate.
For an elliptic model problem, we discuss applications to conforming,
nonconforming and mixed...
We obtain an existence theorem for the problem (0.1) where the coefficients satisfy a degenerate ellipticity condition and hypotheses weaker than the continuity with respect to the variable .
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