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

Champike Attanayake and Deepthika Senaratne

Journal of Mathematics Research, 2024, vol. 15, issue 2, 19

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.

Date: 2024
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