A stochastic collocation method for elliptic partial differential equations with random input data
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.
Risk assessment of dam's running status is an important part of dam management. A data-driven method based on monitored displacement data has been applied in risk assessment, owing to its easy operation and real-time analysis. However, previous data-driven ...
In a recent article [1] we surveyed advances related to adaptation, learning, and optimization over synchronous networks. Various distributed strategies were discussed that enable a collection of networked agents to interact locally in response to streamin ...
In this work, we consider an elliptic partial differential equation (PDE) with a random coefficient solved with the stochastic collocation finite element method (SC-FEM). The random diffusion coefficient is assumed to depend in an affine way on independent ...
In this work, we consider an elliptic partial differential equation with a random coefficient solved with the stochastic collocation finite element method. The random diffusion coefficient is assumed to depend in an affine way on independent random variabl ...
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 ...
In this article, a finite element error analysis is performed on a class of linear and nonlinear elliptic problems with small uncertain input. Using a perturbation approach, the exact (random) solution is expanded up to a certain order with respect to a pa ...
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 ...
In a recent work, Bourgain gave a fine description of the expectation of solutions of discrete linear elliptic equations on Zd with random coefficients in a perturbative regime using tools from harmonic analysis. This result is surprising for it goes beyon ...
We use the averaged variational principle introduced in a recent article on graph spectra [10] to obtain upper bounds for sums of eigenvalues of several partial differential operators of interest in geometric analysis, which are analogues of Kroger's bound ...