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Superconvergence of Modified Nonconforming Cut Finite Element Method for Elliptic Problems

Author

Listed:
  • Xiaoxiao He

    (School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China)

  • Fei Song

    (College of Science, Nanjing Forestry University, Nanjing 210037, China)

Abstract

In this work, we aim to explore the superconvergence of a modified nonconforming cut finite element method with rectangular meshes for elliptic problems. Boundary conditions are imposed via the Nitsche’s method. The superclose property is proven for rectangular meshes. Moreover, a postprocessing interpolation operator is introduced, and it is proven that the postprocessed discrete solution converges to the exact solution, with a superconvergence rate O ( h 3 / 2 ) . Finally, numerical examples are provided to support the theoretical analysis.

Suggested Citation

  • Xiaoxiao He & Fei Song, 2024. "Superconvergence of Modified Nonconforming Cut Finite Element Method for Elliptic Problems," Mathematics, MDPI, vol. 12(16), pages 1-9, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2595-:d:1461754
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