Seminorm estimates for the error
نویسندگان
چکیده
We extend some previous results of our work [1] on the error of the averaging method, in the one-frequency case. The new error estimates apply to any separating family of seminorms on the space of the actions; they generalize our previous estimates in terms of the Euclidean norm. For example, one can use the new approach to get separate error estimates for each action coordinate. An application to rigid body under damping is presented. In a companion paper [2], the same method will be applied to the motion of a satellite around an oblate planet.
منابع مشابه
Direct form seminorms arising in the theory of interpolation by translates of a basis function
In the error analysis of the process of interpolation by translates of a single basis function, certain spaces of functions arise naturally. These spaces are de ned with respect to a seminorm which is given in terms of the Fourier transform of the function. We call this an indirect seminorm. In certain well-understood cases, the seminorm can be rewritten trivially in terms of the function, rath...
متن کاملOn the average principle for one-frequency systems II. Seminorm estimates for the error
We extend some previous results of ours [1] on the error of the averaging method, in the one-frequency case. The new error estimates apply to any separating family of seminorms on the space of the actions; they generalize our previous estimates in terms of the Euclidean norm. For example, one can use as a separating family of seminorms the absolute values of the components of the actions: with ...
متن کاملOptimal A Priori Error Estimates for an Elliptic Problem with Dirac Right-Hand Side
It is well known that finite element solutions for elliptic PDEs with Dirac measures as source terms converge, due to the fact that the solution is not in H1, suboptimal in classical norms. A standard remedy is to use graded meshes, then quasioptimality, i.e., optimal up to a log-factor, for low order finite elements can be recovered, e.g., in the L2-norm. Here we show for the lowest order case...
متن کاملOptimal Mesh for P1 Interpolation in H1 Seminorm
In this paper we present one approach to build optimal meshes for P1 interpolation. Considering classical geometric error estimates based on the Hessian matrix of a solution, we show it is possible to generate optimal meshes in H 1 semi-norm via a simple minimization procedure.
متن کاملEquivalent a posteriori error estimates for spectral element solutions of constrained optimal control problem in one dimension
In this paper, we study spectral element approximation for a constrained optimal control problem in one dimension. The equivalent a posteriori error estimators are derived for the control, the state and the adjoint state approximation. Such estimators can be used to construct adaptive spectral elements for the control problems.
متن کامل