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<p>We study, in two and three dimensional domains, the linear elasticity system under a singular force. The problem is analyzed, in the framework of weighted Sobolev spaces, where the weight belongs to the Muckenhoupt class <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(A_2\)</EquationSource> </InlineEquation>. Based on a simple Finite Element scheme, we design and analyze a residual-type a posteriori error estimator and investigate the reliability and local efficiency properties. Finally, we develop an adaptive method that yields optimal experimental convergence rates for all the numerical examples we perform.</p>

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A posteriori error estimates for the linear elasticity problem with singular sources

  • 期刊论文

  • 发表日期：

    2025年10月6日

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  • Alejandro Allendes,
  • Gilberto Campaña

摘要

We study, in two and three dimensional domains, the linear elasticity system under a singular force. The problem is analyzed, in the framework of weighted Sobolev spaces, where the weight belongs to the Muckenhoupt class \(A_2\) . Based on a simple Finite Element scheme, we design and analyze a residual-type a posteriori error estimator and investigate the reliability and local efficiency properties. Finally, we develop an adaptive method that yields optimal experimental convergence rates for all the numerical examples we perform.