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Research on Convergence rates in Machine Learning research part4

  • We consider the Dirichlet problem for elliptic systems with periodically distributed inclusions with significant contrast compared to the background media.
  • A unified method is developed to quantify convergence rates as the periodicity of inclusions tends to zero and as the parameter approaches either zero or infinity.
  • Based on the obtained convergence rates and a Campanato-type scheme, regularity estimates that are uniform in both periodicity and contrast are derived.
  • The spectral difference method based on p-th order Raviart - Thomas space is studied for the scalar transport equation on regular triangular meshes.

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