<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>596</id>
    <completedYear>2024</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2024-11-15</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Error analysis of a first-order DoD cut cell method for 2D unsteady advection</title>
    <abstract language="eng">In this work we present an a priori error analysis for solving the unsteady advection equation on cut cell meshes along a straight ramp in two dimensions. The space discretization uses a lowest order upwind-type discontinuous Galerkin scheme involving a \textit{Domain of Dependence} (DoD) stabilization to correct the update in the neighborhood of small cut cells. Thereby, it is possible to employ explicit time stepping schemes with a time step length that is independent of the size of the very small cut cells.&#13;
Our error analysis is based on a general framework for error estimates for first-order linear partial differential equations that relies on consistency, boundedness, and discrete dissipation of the discrete bilinear form. We prove these properties for the space discretization involving DoD stabilization. This allows us to prove, for the fully discrete scheme, a quasi-optimal error estimate of order one half in a norm that combines the L∞-in-time L2-in-space norm and a seminorm that contains velocity weighted jumps. We also provide corresponding numerical results.</abstract>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <licence>Creative Commons - CC BY-NC-SA - Namensnennung - Nicht kommerziell -  Weitergabe unter gleichen Bedingungen 4.0 International</licence>
    <author>Gunnar Birke</author>
    <author>Christian Engwer</author>
    <author>Jan Giesselmann</author>
    <author>Sandra May</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cut cell</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>discontinuous Galerkin method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>DoD Stabilization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>a priori error estimate</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>unsteady advection</value>
    </subject>
    <collection role="institutes" number="">Technische Universität Darmstadt</collection>
    <collection role="subprojects" number="">C05</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/596/BirkeEngwerGiesselmannMay20241115.pdf</file>
  </doc>
</export-example>
