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Convergence analysis of a skeletal discontinuous Galerkin finite element method for time-harmonic Maxwell equations with large wave numbers

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  • Dutta Mohapatra, Achyuta Ranjan
  • Deka, Bhupen

Abstract

This article discusses a skeletal discontinuous finite element method for approximating solutions of time-harmonic Maxwell’s equations with high wave numbers. The name justifies the method because the local degrees of freedom are associated with the skeleton of the mesh. These methods are also quite popularly known as the modified weak Galerkin methods. The proposed algorithm for the time-harmonic Maxwell equations is a parameter-free, non-conforming finite element method that uses discontinuous polynomials to approximate the true solution. Due to the choice of functions in these skeletal Galerkin methods, one has the flexibility of an inbuilt weak tangential continuity incorporated in the approximation space. Optimal order of convergence for the errors has been derived in L2 and a discretely defined H(curl)-norms. Numerical computations verify the theoretical convergence rates, and the proposed numerical approximation scheme is stable for the time-harmonic equations with large wave numbers.

Suggested Citation

  • Dutta Mohapatra, Achyuta Ranjan & Deka, Bhupen, 2026. "Convergence analysis of a skeletal discontinuous Galerkin finite element method for time-harmonic Maxwell equations with large wave numbers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 243(C), pages 407-426.
    • Handle: RePEc:eee:matcom:v:243:y:2026:i:c:p:407-426
    DOI: 10.1016/j.matcom.2025.11.039
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