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We derive computable a posteriori error estimates for the lowest order nonconforming Crouzeix–Raviart element applied to the approximation of incompressible Stokes flow. The estimator provides an explicit upper bound that is free of any unknown constants, provided that a reasonable lower bound for the inf-sup constant of the underlying problem is available.(More)
The saturation assumption asserts that the best approximation error inH1 0 with piecewise quadratic finite elements is strictly smaller than that of piecewise linear finite elements. We establish a link between this assumption and the oscillation of f = −∆u, and prove that small oscillation relative to the best error with piecewise linears implies the(More)
In this article we study the settling process of a colloidal particle under the influence of a gravitational or centrifugal field in an unbounded electrolyte solution. Since particles in aqueous solutions normally carry a non-zero surface charge, a microscopic electric field develops which alters the sedimentation process compared to an uncharged particle.(More)
We derive a posteriori error estimates for the approximation of linear elliptic problems on domains with piecewise smooth boundary. The numerical solution is assumed to be defined on a Finite Element mesh, whose boundary vertices are located on the boundary of the continuous problem. No assumption is made on a geometrically fitting shape. A posteriori error(More)
We develop a new analysis for residual-type a posteriori error estimation for a class of highly indefinite elliptic boundary value problems by considering the Helmholtz equation at high wavenumber k > 0 as our model problem. We employ classical conforming Galerkin discretization by using hp-finite elements. The key role in the analysis is played by a new(More)
We present quantitative reconstructions of regional vegetation cover in north-western Europe, western Europe north of the Alps, and eastern Europe for five time windows in the Holocene [around 6k, 3k, 0.5k, 0.2k, and 0.05k calendar years before present (bp)] at a 1° × 1° spatial scale with the objective of producing vegetation descriptions suitable for(More)
We introduce a space-time discretization for linear first-order hyperbolic evolution systems using a discontinuous Galerkin approximation in space and a Petrov–Galerkin scheme in time. We show well-posedness and convergence of the discrete system. Then we introduce an adaptive strategy based on goal-oriented dual-weighted error estimation. The full(More)
Lab-on-a-chip systems made of polymers are promising for the integration of active optical elements, enabling e.g. on-chip excitation of fluorescent markers or spectroscopy. In this work we present diffusion operation of tunable optofluidic dye lasers in a polymer foil. We demonstrate that these first order distributed feedback lasers can be operated for(More)
Out-of-plane gap solitons in 2D photonic crystals are optical beams localized in the plane of periodicity of the medium and delocalized in the orthogonal direction, in which they propagate with a nonzero velocity. We study such gap solitons as described by the Kerr nonlinear Maxwell system. Using a model of the nonlinear polarization, which does not(More)