A Spatially and Temporally Second Order Method for Solving Parabolic Interface Problems

Presenter and Co-Authors

Kumudu Gamage, Old Dominion UniversityFollow
Yan Peng, Old Dominion University

College

College of Sciences

Department

Mathematics and Statistics

Graduate Level

Doctoral

Graduate Program/Concentration

Computational Applied Mathematics

Publication Date

4-2022

DOI

10.25883/ayzx-mn43

Abstract

Parabolic interface problems have many applications in physics and biology, such as hyperthermia treatment of cancer, underground water flow, and food engineering. Here we present an algorithm for solving two-dimensional parabolic interface problems where the coefficient and the forcing term have a discontinuity across the interface. The Crank-Nicolson scheme is used for time discretization, and the direct immersed interface method is used for spatial discretization. The proposed method is second order in both space and time for both solution and gradients in maximum norm.

Keywords

Parabolic interface problems, Immersed interface method

Disciplines

Numerical Analysis and Computation | Partial Differential Equations

Files

Recommended Citation

Gamage, Kumudu and Peng, Yan, "A Spatially and Temporally Second Order Method for Solving Parabolic Interface Problems" (2022). College of Sciences Posters. 6.
https://digitalcommons.odu.edu/gradposters2022_sciences/6