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Convergence for an Immersed Finite Volume Method for Elliptic and Parabolic Interface Problems

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  • Champike Attanayake
  • Deepthika Senaratne

Abstract

In this article we analyze an immersed interface finite volume method for second order elliptic and parabolic interface problems. We show the optimal convergence of the elliptic interface problem in L^2 and energy norms. For the parabolic interface problem, we prove the optimal order in L^2 and energy norms for piecewise constant and variable diffusion coefficients respectively. Furthermore, for the elliptic interface problem, we demonstrate super convergence at element nodes when the diffusion coefficient is a piecewise constant. Numerical examples are also provided to confirm the optimal error estimates.

Suggested Citation

  • Champike Attanayake & Deepthika Senaratne, 2024. "Convergence for an Immersed Finite Volume Method for Elliptic and Parabolic Interface Problems," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 15(2), pages 1-19, December.
    • Handle: RePEc:ibn:jmrjnl:v:15:y:2024:i:2:p:19
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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