A mathematical model of steady state heat conduction is of an elliptic nature in a composite elliptic interface medium and arises in various areas of science and engineering. The steady state heat conduction in layered bodies is one of the largest areas of applications of elliptic interface problems. In this article, we propose a numerical approach based on the Extended Finite Element method on uniform mesh for this interface problem with second order accuracy in H¹-norm and first order accuracy in L²-norm. To show the accuracy of our approach we have solved interface problem with interface and discuss the behavior of our solutions by comparing with FEM solutions.

elliptic interface problems, extended finite element method, finite difference method, steady state heat conduction, immersed interface method.

Received: February 15, 2021; Accepted: March 16, 2021; Published: March 19, 2021

How to cite this article: Akanksha Srivastava and Nita H. Shah, Mathematical Modelling and Computer Simulation of Two Dimensional Steady State Heat Conduction Problem by Extended Finite Element Method, Advances and Applications in Fluid Mechanics 26(1) (2021), 67-84. DOI: 10.17654/FM026010067

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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