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June 27, 2026Computational Methods in Applied Mathematics

A Reduced Weak Galerkin Finite Element Formulation Based on the POD Method for a Semilinear Parabolic Equation

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Authors

ZZZihan ZhengFGFuzheng GaoJCJintao Cui

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Overview

Randomized trial demonstrates optimal error estimates in a reduced-order model, suggesting efficiency in solving parabolic equations.

Key Points

  • This work aims to develop a reduced-order model for a semilinear parabolic equation using POD.
  • Utilized the weak Galerkin finite element method for spatial discretization.
  • Applied the Crank–Nicolson scheme for temporal discretization.
  • Established optimal error estimates and confirmed the model's accuracy.
  • Achieved second-order accuracy in time and O(h^{k+1}) accuracy in space under L^2 norm.
  • Demonstrated significant reduction in degrees of freedom.
  • Confirmed consistency between numerical results and theoretical predictions.

Cite This Study

Zheng et al. (2026) studied this question.

synapsesocial.com/papers/6a3f68cdaea7db3c1953fbdbhttps://doi.org/10.1515/cmam-2025-0194
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