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<p>The paper presents an <i>hp</i> analysis of Nitsche’s method applied to Maxwell’s problem using a stabilised finite element (FE) formulation. While the FE formulation and the weak imposition of Dirichlet boundary conditions have been previously explored, the novelty of this work lies in the <i>hp</i> mesh refinement analysis, examining the method’s behaviour as both the mesh size <i>h</i> decreases and the polynomial order <i>p</i> increases. The study specifically aims to adapt previous analyses to account for these refinements and to highlight a slight lack of optimality in <i>p</i> that is intrinsic to Nitsche’s method.</p>

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hp Analysis of Nitsche’s method for Maxwell’s problem using a stabilised finite element formulation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年8月1日

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  • Daniele Boffi,
  • Ramon Codina,
  • Önder Türk

摘要

The paper presents an hp analysis of Nitsche’s method applied to Maxwell’s problem using a stabilised finite element (FE) formulation. While the FE formulation and the weak imposition of Dirichlet boundary conditions have been previously explored, the novelty of this work lies in the hp mesh refinement analysis, examining the method’s behaviour as both the mesh size h decreases and the polynomial order p increases. The study specifically aims to adapt previous analyses to account for these refinements and to highlight a slight lack of optimality in p that is intrinsic to Nitsche’s method.