In this paper we give a global characterisation of classes of ultradifferentiable functions and corresponding ultradistributions on a compact manifold X. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on X. This extends the result for analytic functions on compact manifold by Seeley [See69], and the characterisation of Gevrey functions and Gevrey u...

Abstract We derive optimal and asymptotically exact a posteriori error estimates for the approximation of eigenfunction Laplace eigenvalue problem. To do so, we combine two results from literature. First, use hypercircle techniques developed mixed approximations with Raviart-Thomas finite elements. In addition, post-processings introduced based on Brezzi-Douglas-Marini element. these approaches...

The rnapshot method is used to analyze a large eddy simulation of axisymmetric jet flow. An ensemble of realizations is collected using a sampling condition that corresponds to the passage of a large scale vortex at a position six diameters downstream from the nozzle. The analysis is performed separately on a variable composed of the primitive flow quantities and the mass fraction of the materi...