Search results for "Superconvergence"
showing 10 items of 11 documents
On a global superconvergence of the gradient of linear triangular elements
1987
Abstract We study a simple superconvergent scheme which recovers the gradient when solving a second-order elliptic problem in the plane by the usual linear elements. The recovered gradient globally approximates the true gradient even by one order of accuracy higher in the L 2 -norm than the piecewise constant gradient of the Ritz—Galerkin solution. A superconvergent approximation to the boundary flux is presented as well.
On finite element approximation of the gradient for solution of Poisson equation
1981
A nonconforming mixed finite element method is presented for approximation of ?w with Δw=f,w| r =0. Convergence of the order $$\left\| {\nabla w - u_h } \right\|_{0,\Omega } = \mathcal{O}(h^2 )$$ is proved, when linear finite elements are used. Only the standard regularity assumption on triangulations is needed.
A mixed finite element method for the heat flow problem
1981
A semidiscrete finite element scheme for the approximation of the spatial temperature change field is presented. The method yields a better order of convergence than the conventional use of linear elements.
Superconvergent Perturbation Theory, KAM Theorem (Introduction)
2001
Here we are dealing with an especially fast converging perturbation series, which is of particular importance for the proof of the KAM theorem (cf. below).
finite element methods
2017
Two robot patch recovery methods with built-in field equations and boundary conditions superconvergence similarities in standard and mixed finite element methods on the FEM for the Navier-Stokes equations in the domains with corner singularities projections in finite element analysis and application element analysis method and superconvergence quadratic interpolation polynomials in vertices of strongly regular triangulations explicit error bounds for a nonconforming finite element method analysis of the average efficiency of an error estimator on the mesh for difference schemes of higher accuracy for the heat-conduction equation shape design sensitivity formulae approximated by means of a r…
On superconvergence techniques
1987
A brief survey with a bibliography of superconvergence phenomena in finding a numerical solution of differential and integral equations is presented. A particular emphasis is laid on superconvergent schemes for elliptic problems in the plane employing the finite element method.
Optimized time-dependent perturbation theory for pulse-driven quantum dynamics in atomic or molecular systems
2003
We present a time-dependent perturbative approach adapted to the treatment of intense pulsed interactions. We show there is a freedom in choosing secular terms and use it to optimize the accuracy of the approximation. We apply this formulation to a unitary superconvergent technique and improve the accuracy by several orders of magnitude with respect to the Magnus expansion.
Unitary time-dependent superconvergent technique for pulse-driven quantum dynamics
2003
We present a superconvergent Kolmogorov-Arnold-Moser type of perturbation theory for time-dependent Hamiltonians. It is strictly unitary upon truncation at an arbitrary order and not restricted to periodic or quasiperiodic Hamiltonians. Moreover, for pulse-driven systems we construct explicitly the KAM transformations involved in the iterative procedure. The technique is illustrated on a two-level model perturbed by a pulsed interaction for which we obtain convergence all the way from the sudden regime to the opposite adiabatic regime.
Superconvergence phenomenon in the finite element method arising from averaging gradients
1984
We study a superconvergence phenomenon which can be obtained when solving a 2nd order elliptic problem by the usual linear elements. The averaged gradient is a piecewise linear continuous vector field, the value of which at any nodal point is an average of gradients of linear elements on triangles incident with this nodal point. The convergence rate of the averaged gradient to an exact gradient in theL 2-norm can locally be higher even by one than that of the original piecewise constant discrete gradient.
Postprocessing of a Finite Element Scheme with Linear Elements
1987
In this contribution we first give a brief survey of postprocessing techniques for accelerating the convergence of finite element schemes for elliptic problems. We also generalize a local superconvergence technique recently analyzed by Křižek and Neittaanmaki ([20]) to a global technique. Finally, we show that it is possible to obtain O(h4) accuracy for the gradient in some cases when only linear elements are used. Numerical tests are presented.