MATHICSE Technical Report : Convergence of quasi-optimal stochastic Galerkin methods for a class of PDES with random coefficients
Related publications (35)
Graph Chatbot
Chat with Graph Search
Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.
DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.
This paper examines the minimization of the cost for an expected random production output, given an assembly of finished goods from two random inputs, matched in two categories. We describe the optimal input portfolio, first using the standard normal appro ...
In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...
In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method ...
In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain ...
This thesis is devoted to the derivation of error estimates for partial differential equations with random input data, with a focus on a posteriori error estimates which are the basis for adaptive strategies. Such procedures aim at obtaining an approximati ...
Finite elements methods (FEMs) have benefited from decades of development to solve partial differential equations (PDEs) and to simulate physical systems. In the recent years, machine learning (ML) and artificial neural networks (ANN) have shown great pote ...
The numerical solution of partial differential equations (PDEs) depending on para- metrized or random input data is computationally intensive. Reduced order modeling techniques, such as the reduced basis methods, have been developed to alleviate this compu ...
The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes ...
We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of term ...
We perform a general optimization of the parameters in the multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation orders and computational costs. We optimize hierarchies with geometric and ...