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<p>We extend a distributed finite element method built upon model order reduction to arbitrary polynomial degree using a hybrid Nitsche scheme. The new method considerably simplifies the transformation of the finite element system to the reduced basis for large problems. We prove that the error of the reduced Nitsche solution converges optimally with respect to the approximation order of the finite element spaces and linearly with respect to the dimension reduction parameter. Numerical tests with nontrivial tetrahedral meshes using second-degree polynomial bases support the theoretical results.</p>

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Hybrid Nitsche method for distributed computing

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月2日

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  • Tom Gustafsson,
  • Antti Hannukainen,
  • Vili Kohonen,
  • Juha Videman

摘要

We extend a distributed finite element method built upon model order reduction to arbitrary polynomial degree using a hybrid Nitsche scheme. The new method considerably simplifies the transformation of the finite element system to the reduced basis for large problems. We prove that the error of the reduced Nitsche solution converges optimally with respect to the approximation order of the finite element spaces and linearly with respect to the dimension reduction parameter. Numerical tests with nontrivial tetrahedral meshes using second-degree polynomial bases support the theoretical results.