<mods:mods xmlns:mods="http://www.loc.gov/mods/v3" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:METS="http://www.loc.gov/METS/" ID="etd595" xsi:schemaLocation="http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd">
          <mods:titleInfo>
            <mods:title>Effective approximations of stochastic partial differential equations based on Wiener chaos expansions and the Malliavin calculus</mods:title>
          </mods:titleInfo>
          <mods:name type="personal">
            <mods:namePart>Lee, Chia Ying </mods:namePart>
            <mods:role>
              <mods:roleTerm type="text">creator</mods:roleTerm>
            </mods:role>
          </mods:name>
          <mods:originInfo>
            <mods:copyrightDate>2011</mods:copyrightDate>
          </mods:originInfo>
          <mods:physicalDescription>
            <mods:extent>x, 125 p.</mods:extent>
            <mods:digitalOrigin>born digital</mods:digitalOrigin>
          </mods:physicalDescription>
          <mods:note>Thesis (Ph.D. -- Brown University (2011)</mods:note>
          <mods:name type="personal">
            <mods:namePart>Rozovsky, Boris</mods:namePart>
            <mods:role>
              <mods:roleTerm type="text">Director</mods:roleTerm>
            </mods:role>
          </mods:name>
          <mods:name type="personal">
            <mods:namePart>Karniadakis, George</mods:namePart>
            <mods:role>
              <mods:roleTerm type="text">Reader</mods:roleTerm>
            </mods:role>
          </mods:name>
          <mods:name type="personal">
            <mods:namePart>Ramanan, Kavita</mods:namePart>
            <mods:role>
              <mods:roleTerm type="text">Reader</mods:roleTerm>
            </mods:role>
          </mods:name>
          <mods:name type="corporate">
            <mods:namePart>Brown University. Applied Mathematics</mods:namePart>
            <mods:role>
              <mods:roleTerm type="text">sponsor</mods:roleTerm>
            </mods:role>
          </mods:name>
          <mods:genre authority="aat">theses</mods:genre>
          <mods:abstract>This thesis studies the application of the Wiener chaos expansion in the analysis of stochastic partial differential equations (SPDEs). Specifically, linear parabolic SPDEs and the quantized stochastic Navier-Stokes equations are considered, under the framework of the Malliavin calculus. Especially for these highly singular SPDEs, the Wiener chaos expansion is a useful tool for our study of the basic questions of solvability, regularity and dynamical behaviour, and it enables us to study approximations of the solutions of SPDEs and to quantify the errors of approximation. For the quantized stochastic Navier-Stokes equations, we use the Malliavin calculus to formulate a random perturbation of the Navier-Stokes equations that is unbiased, and we will show the existence and uniqueness of steady and time-dependent solutions, as well as the convergence to steady solution, in a stochastic weighted space. We also study a stochastic finite element method for numerical simulation of the solution of linear parabolic SPDEs and derive error estimates for the numerical solution. Finally, we show how one basis of the Wiener chaos expansion can be more efficient than another for approximating the energy of the solution, so that computational efficiency can be increased when applied to some physical applications.</mods:abstract>        
  <mods:subject>
            <mods:topic>Wiener chaos expansion</mods:topic>
          </mods:subject>
          <mods:subject>
            <mods:topic>stochastic finite element method</mods:topic>
          </mods:subject>
          <mods:subject>
            <mods:topic>stochastic Navier-Stokes equation</mods:topic>
          </mods:subject>
          <mods:subject authority="FAST" authorityURI="http://id.worldcat.org/fast" valueURI="http://id.worldcat.org/fast/1133516"><mods:topic>Stochastic partial differential equations</mods:topic></mods:subject><mods:subject authority="FAST" authorityURI="http://id.worldcat.org/fast" valueURI="http://id.worldcat.org/fast/1006757"><mods:topic>Malliavin calculus</mods:topic></mods:subject><mods:recordInfo>
            <mods:recordContentSource authority="marcorg">RPB</mods:recordContentSource>
            <mods:recordCreationDate encoding="iso8601">20111003</mods:recordCreationDate>
          </mods:recordInfo>
        <mods:language><mods:languageTerm type="code" authority="iso639-2b">eng</mods:languageTerm><mods:languageTerm type="text">English</mods:languageTerm></mods:language><mods:identifier type="doi">10.7301/Z0FJ2F2N</mods:identifier><mods:accessCondition type="rights statement" xlink:href="http://rightsstatements.org/vocab/InC/1.0/">In Copyright</mods:accessCondition><mods:accessCondition type="restriction on access">Collection is open for research.</mods:accessCondition><mods:typeOfResource authority="primo">dissertations</mods:typeOfResource></mods:mods>