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<p>This paper discusses and examines a Virtual Element Method (VEM) in mixed form for discretizing a strongly damped wave equation within a bounded region in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>. The analysis includes establishing optimal convergence rates for both semi-discrete and fully discrete methods using estimates from a novel mixed intermediate projection. Using the enhanced regularity of the displacement <i>u</i>, the discrete solution’s super-convergence is demonstrated. Additionally, theoretical results are validated through numerous numerical experiments. The influence of the damping factor <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> on the system’s energy is also demonstrated.</p>

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Mixed Virtual Element Method for a Strongly Damped Wave Equation

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Meghana Suthar,
  • Ankit Kumar,
  • Sangita Yadav

摘要

This paper discusses and examines a Virtual Element Method (VEM) in mixed form for discretizing a strongly damped wave equation within a bounded region in \(\mathbb {R}^2\) R 2 . The analysis includes establishing optimal convergence rates for both semi-discrete and fully discrete methods using estimates from a novel mixed intermediate projection. Using the enhanced regularity of the displacement u, the discrete solution’s super-convergence is demonstrated. Additionally, theoretical results are validated through numerous numerical experiments. The influence of the damping factor \(\alpha \) α on the system’s energy is also demonstrated.