Open Access

ARTICLE

An Augmented IB Method & Analysis for Elliptic BVP on Irregular Domains

Zhilin Li^1,∗, Baiying Dong², Fenghua Tong³, Weilong Wang³

1 CRSC & Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA.
2 School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China.
3 College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, China.
* Corresponding Author: Zhilin Li. Email: zhilin@math.ncsu.edu.

(This article belongs to the Special Issue: Recent Developments of Immersed Methods for Fluid-structure Interactions)

Computer Modeling in Engineering & Sciences 2019, 119(1), 63-72. https://doi.org/10.32604/cmes.2019.04635

Abstract

The immersed boundary method is well-known, popular, and has had vast areas of applications due to its simplicity and robustness even though it is only first order accurate near the interface. In this paper, an immersed boundary-augmented method has been developed for linear elliptic boundary value problems on arbitrary domains (exterior or interior) with a Dirichlet boundary condition. The new method inherits the simplicity, robustness, and first order convergence of the IB method but also provides asymptotic first order convergence of partial derivatives. Numerical examples are provided to confirm the analysis.

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Keywords

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