Open Advanced Search

Log in
Enterprise Plans
Sign Up

Log in
Sign Up
Enterprise Plans
Browse
Features
Pricing

DeepDyve

Advanced Search

show/hide query preview

With all of the words or DOIs:

DeepDyve's default query mode: search by keyword or DOI.

With the exact phrase:

Require these words, in this exact order. Do not surround your terms in double-quotes ("") in this field.

With at least one of the words:

Find any of these words, separated by spaces

Without the words:

Exclude each of these words, separated by spaces

With words in the article title:

Search for these terms only in the title of an article

Published between the years:

With the following authors:

Most effective as: LastName, First Name or Lastname, FN

With words in the journal name:

Search for articles published in journals where these words are in the journal name

Reset filters

Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

DeepDyve requires Javascript to function. Please enable Javascript on your browser to continue.

Polynomial Chaos Methods for Hyperbolic Partial Differential Equations

Part of the Mathematical Engineering Book Series

DOI: 10.1007/978-3-319-10714-1

ISBN: 978-3-319-10713-4

Publisher: Springer International Publishing - Springer Journals

Sep 17, 2014

1 - 9 of 9 Chapters

LitStream

Introduction

Pettersson, Mass Per; Iaccarino, Gianluca; Nordström, Jan

Pages: 3 –9

[In many physical problems, knowledge is limited in quality and quantity by variability, bias in the measurements and limitations in the measurements: these are all sources of uncertaintiesuncertainties. When we attempt to solve the problem numerically, we must account for those limitations, and...
LitStream

Random Field Representation

Pettersson, Mass Per; Nordström, Jan; Iaccarino, Gianluca

Pages: 11 –21

[Nonlinear conservation laws subject to uncertainty are expected to develop solutions that are discontinuous in spatial as well as in stochastic dimensions. In order to allow piecewise continuous solutions to the problems of interest, we follow [7] and broaden the concept of solutions to the...
LitStream

Polynomial Chaos Methods

Pettersson, Mass Per; Iaccarino, Gianluca; Nordström, Jan

Pages: 23 –29

[In this chapter we review methods for formulating partial differential equations based on the random field representations outlined in Chap. 2 These include the stochastic Galerkin method, which is the predominant choice in this book, as well as other methods that frequently occur in the...
LitStream

Numerical Solution of Hyperbolic Problems

Pettersson, Mass Per; Iaccarino, Gianluca; Nordström, Jan

Pages: 31 –44

[In this chapter, we introduce spatial discretization schemes for systems of conservation laws. For smooth problems, summation-by-parts operators with weak enforcement of boundary conditions allow for the design of stable high-order accurate schemes. Summation by parts is the discrete equivalent...
LitStream

Linear Transport Under Uncertainty

Pettersson, Mass Per; Iaccarino, Gianluca; Nordström, Jan

Pages: 47 –80

[This chapter aims to present accurate and stable numerical schemes for the solution of a class of linear diffusive transport problems. The advection-diffusion equation subject to uncertain viscosity with known statistical description is represented by a spectral expansion in the stochastic...
LitStream

Nonlinear Transport Under Uncertainty

Pettersson, Mass Per; Iaccarino, Gianluca; Nordström, Jan

Pages: 81 –109

[Burgers’ equation is an interesting and non-linear model problem from which, many results can be extended to other hyperbolic systems, e.g., the Euler equations. In this chapter, a detailed uncertainty quantification analysis is performed for the Burgers’ equation; we employ a spectral...
LitStream

Boundary Conditions and Data

Pettersson, Mass Per; Iaccarino, Gianluca; Nordström, Jan

Pages: 111 –121

[We continue analysis of Burgers’ equation from the previous chapter with a focus on the effect of data for the boundaryboundary conditions conditions. To facilitate understanding, we deal only with the truncated representation u(x,t,ξ)=u0ψ0+u1ψ1\documentclass[12pt]{minimal}...
LitStream

gPC for the Euler Equations

Pettersson, Mass Per; Iaccarino, Gianluca; Nordström, Jan

Pages: 125 –148

[We present a stochastic Galerkin formulation of the Euler equations based on the variables introduced by P. L. Roe in 1981 for the well-known and widely used Roe solver. For numerical discretization, a Roe average matrix for the standard MUSCL-Roe scheme with Roe variables is derived. The Roe...
LitStream

A Hybrid Scheme for Two-Phase Flow

Pettersson, Mass Per; Iaccarino, Gianluca; Nordström, Jan

Pages: 149 –172

[In this chapter, we investigate a two-phase flow generalization of the Euler equations. A symmetrized problem formulation that generalizes previous energy estimates in for the Euler equations is used for the stochastic Galerkin system. The solution is expected to develop non-smooth features that...

results per page

Browse All eBooks

Features

Search and discover articles on DeepDyve, PubMed, and Google Scholar
Read the full-text of open access and premium content
Organize articles with folders and bookmarks
Collaborate on and share articles and folders

Info

Pricing
Enterprise Plans
Browse Journals & Topics
About DeepDyve

Help

Help
Publishers
Contact Us

Sign up for your DeepDyve account now!

Read and print from thousands of top scholarly journals.

System error. Please try again!

Continue with Facebook

By signing up, you agree to DeepDyve’s Terms of Service and Privacy Policy.

Already have an account? Log in

Save Article to Bookmarks

Bookmark this article. You can see your Bookmarks on your DeepDyve Library.

To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.

Subscribe to Journal Email Alerts

To subscribe to email alerts, please log in first, or sign up for a DeepDyve account if you don’t already have one.

Follow a Journal

To get new article updates from a journal on your personalized homepage, please log in first, or sign up for a DeepDyve account if you don’t already have one.

Our policy towards the use of cookies

All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.

cookie policy