Projection Methods With Différent Trial and Test Spaces
نویسنده
چکیده
We consider finite element projection methods for linear partial differential equations, in which the spaces of trial functions and test functions may be different. In addition to approximation and smoothness properties, conditions implying equality of dimensions and uniform coerciveness are required, the most important of which resembles a strong form of an inverse assumption. Our results provide a mechanism for the difference in the rate of convergence of Galerkin procedures with cubic splines and Hermite cubics, applied to first order symmetric hyperbolic problems [13].
منابع مشابه
Paracompactness on supra topological spaces
In this article, we present the concept of supra paracompact spaces and study its basic properties. We elucidate its relationship with supra compact spaces and prove that the property of being a supra paracompact space is weakly hereditary and topological properties. Also, we provide some examples to show some results concerning paracompactness on topology are invalid on supra topology. Finally...
متن کاملA Geometry Preserving Kernel over Riemannian Manifolds
Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...
متن کاملApproximating fixed points for nonexpansive mappings and generalized mixed equilibrium problems in Banach spaces
We introduce a new iterative scheme for nding a common elementof the solutions set of a generalized mixed equilibrium problem and the xedpoints set of an innitely countable family of nonexpansive mappings in a Banachspace setting. Strong convergence theorems of the proposed iterative scheme arealso established by the generalized projection method. Our results generalize thecorresponding results...
متن کاملRandom Positive-Only Projections: PPMI-Enabled Incremental Semantic Space Construction
We introduce positive-only projection (PoP), a new algorithm for constructing semantic spaces and word embeddings. The PoP method employs random projections. Hence, it is highly scalable and computationally efficient. In contrast to previous methods that use random projection matrices R with the expected value of 0 (i.e., E(R) = 0), the proposed method uses R with E(R) > 0. We use Kendall’s τb ...
متن کاملNew hybrid method for equilibrium problems and relatively nonexpansive mappings in Banach spaces
In this paper, applying hybrid projection method, a new modified Ishikawa iteration scheme is presented for finding a common element of the solution set of an equilibrium problem and the set of fixed points of relatively nonexpansive mappings in Banach spaces. A numerical example is given and the numerical behaviour of the sequences generated by this algorithm is compared with several existence...
متن کامل