FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1967117214> ?p ?o ?g. }

• W1967117214 endingPage "536" @default.
• W1967117214 startingPage "493" @default.
• W1967117214 abstract "In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and depends on a finite number of random variables. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. This approach leads to the solution of uncoupled deterministic problems as in the Monte Carlo method. We consider both full and sparse tensor product spaces of orthogonal polynomials. We provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points for full and sparse tensor product spaces and under some regularity assumptions on the data. In particular, we show that, unlike in elliptic and parabolic problems, the solution to hyperbolic problems is not in general analytic with respect to the random variables. Therefore, the rate of convergence may only be algebraic. An exponential/fast rate of convergence is still possible for some quantities of interest and for the wave solution with particular types of data. We present numerical examples, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo method for this class of problems." @default.
• W1967117214 created "2016-06-24" @default.
• W1967117214 creator A5004939553 @default.
• W1967117214 creator A5043766972 @default.
• W1967117214 creator A5047447127 @default.
• W1967117214 date "2012-08-31" @default.
• W1967117214 modified "2023-10-16" @default.
• W1967117214 title "A stochastic collocation method for the second order wave equation with a discontinuous random speed" @default.
• W1967117214 cites W1538934584 @default.
• W1967117214 cites W1973195575 @default.
• W1967117214 cites W1982421072 @default.
• W1967117214 cites W1982867713 @default.
• W1967117214 cites W1983156129 @default.
• W1967117214 cites W1985681033 @default.
• W1967117214 cites W1991160236 @default.
• W1967117214 cites W2002926750 @default.
• W1967117214 cites W2004814202 @default.
• W1967117214 cites W2018159038 @default.
• W1967117214 cites W2027748639 @default.
• W1967117214 cites W2051926042 @default.
• W1967117214 cites W2053750683 @default.
• W1967117214 cites W2055460625 @default.
• W1967117214 cites W2056227133 @default.
• W1967117214 cites W2058362163 @default.
• W1967117214 cites W2061604462 @default.
• W1967117214 cites W2064332562 @default.
• W1967117214 cites W2065588677 @default.
• W1967117214 cites W2070021957 @default.
• W1967117214 cites W2072282162 @default.
• W1967117214 cites W2083845086 @default.
• W1967117214 cites W2113517083 @default.
• W1967117214 cites W2123196638 @default.
• W1967117214 cites W2142678007 @default.
• W1967117214 cites W2142863015 @default.
• W1967117214 cites W2143591652 @default.
• W1967117214 cites W2150093340 @default.
• W1967117214 cites W2155432414 @default.
• W1967117214 cites W2163299986 @default.
• W1967117214 cites W2321957512 @default.
• W1967117214 cites W2333857658 @default.
• W1967117214 cites W3111685920 @default.
• W1967117214 cites W4229739412 @default.
• W1967117214 cites W4231538119 @default.
• W1967117214 cites W4247375400 @default.
• W1967117214 cites W4299587901 @default.
• W1967117214 cites W4301386114 @default.
• W1967117214 doi "https://doi.org/10.1007/s00211-012-0493-5" @default.
• W1967117214 hasPublicationYear "2012" @default.
• W1967117214 type Work @default.
• W1967117214 sameAs 1967117214 @default.
• W1967117214 citedByCount "47" @default.
• W1967117214 countsByYear W19671172142012 @default.
• W1967117214 countsByYear W19671172142014 @default.
• W1967117214 countsByYear W19671172142015 @default.
• W1967117214 countsByYear W19671172142016 @default.
• W1967117214 countsByYear W19671172142017 @default.
• W1967117214 countsByYear W19671172142018 @default.
• W1967117214 countsByYear W19671172142019 @default.
• W1967117214 countsByYear W19671172142020 @default.
• W1967117214 countsByYear W19671172142021 @default.
• W1967117214 countsByYear W19671172142022 @default.
• W1967117214 countsByYear W19671172142023 @default.
• W1967117214 crossrefType "journal-article" @default.
• W1967117214 hasAuthorship W1967117214A5004939553 @default.
• W1967117214 hasAuthorship W1967117214A5043766972 @default.
• W1967117214 hasAuthorship W1967117214A5047447127 @default.
• W1967117214 hasBestOaLocation W19671172142 @default.
• W1967117214 hasConcept C10138342 @default.
• W1967117214 hasConcept C119857082 @default.
• W1967117214 hasConcept C134306372 @default.
• W1967117214 hasConcept C162324750 @default.
• W1967117214 hasConcept C182306322 @default.
• W1967117214 hasConcept C28826006 @default.
• W1967117214 hasConcept C33923547 @default.
• W1967117214 hasConcept C41008148 @default.
• W1967117214 hasConcept C48753275 @default.
• W1967117214 hasConcept C59696629 @default.
• W1967117214 hasConcept C80023036 @default.
• W1967117214 hasConceptScore W1967117214C10138342 @default.
• W1967117214 hasConceptScore W1967117214C119857082 @default.
• W1967117214 hasConceptScore W1967117214C134306372 @default.
• W1967117214 hasConceptScore W1967117214C162324750 @default.
• W1967117214 hasConceptScore W1967117214C182306322 @default.
• W1967117214 hasConceptScore W1967117214C28826006 @default.
• W1967117214 hasConceptScore W1967117214C33923547 @default.
• W1967117214 hasConceptScore W1967117214C41008148 @default.
• W1967117214 hasConceptScore W1967117214C48753275 @default.
• W1967117214 hasConceptScore W1967117214C59696629 @default.
• W1967117214 hasConceptScore W1967117214C80023036 @default.
• W1967117214 hasIssue "3" @default.
• W1967117214 hasLocation W19671172141 @default.
• W1967117214 hasLocation W19671172142 @default.
• W1967117214 hasOpenAccess W1967117214 @default.
• W1967117214 hasPrimaryLocation W19671172141 @default.
• W1967117214 hasRelatedWork W1964708246 @default.
• W1967117214 hasRelatedWork W1984357102 @default.
• W1967117214 hasRelatedWork W2027346437 @default.
• W1967117214 hasRelatedWork W2027647883 @default.

• next