Alexey Chernov

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Article Accepted Version Chernov, A. (2012) Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex. It is advisable to refer to the publisher's version if you intend to cite from the work. All outputs in CentAUR are protected by Intellectual Property Rights law, including copyright law. Copyright and IPR is(More)
It is advisable to refer to the publisher's version if you intend to cite from the work. Abstract. Galerkin discretizations of integral operators in R d require the evaluation of integrals S (1) S (2) f (x, y) dydx,w h e r eS (1) ,S (2) are d-dimensional simplices and f has a singularity at x = y. In [A. Chernov, T. von Petersdorff, and C. Schwab, M2A NM a(More)
We extend the general framework of the Multilevel Monte Carlo method to multilevel estimation of arbitrary order central statistical moments. In particular, we prove that under certain assumptions, the total cost of a MLMC central moment estimator is asymptotically the same as the cost of the multilevel sample mean estimator and thereby is asymptotically(More)
We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(α, u) = 0 for random input(More)
In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L and tensorized H 0 simultaneously on a standard k-dimensional cube. In(More)
Galerkin discretizations of integral operators in R d require the evaluation of integrals R S (1) R S (2) f (x, y) dydx where S (1) , S (2) are d-dimensional simplices and f has a singularity at x = y. In [3] we constructed a family of hp-quadrature rules Q N with N function evaluations for a class of integrands f allowing for algebraic singularities at x =(More)
In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d ≥ 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases(More)