Immersed Interface Method for elliptic equations based on a piecewise second order polynomial

Authors:
Jianping Zhao;Yanren Hou;Yongfei Li
Affiliations:
Faculty of Science, Xi'an Jiaotong University, Xi'an, Shanxi, 710049, China and College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, China;Faculty of Science, Xi'an Jiaotong University, Xi'an, Shanxi, 710049, China;Faculty of Science, Xi'an Jiaotong University, Xi'an, Shanxi, 710049, China
Venue:
Computers & Mathematics with Applications
Year:
2012

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Abstract

In this paper, we develop finite difference methods for elliptic equations in a domain @W@?R^d, d=1,2. Within the region @W, we suppose there is an irregular surface @C of codimension 1 (hereafter called an interface) across which the function u or some of its derivatives are known to be discontinuous. We use uniform grid and a piecewise second order polynomial to approximate u, then we get a second order method for these problems. At last, we give several examples to show the correctness and efficiency of the scheme.