TY - JOUR
T1 - Convergence of boundary integral method for a free boundary system
AU - Hao, Wenrui
AU - Hu, Bei
AU - Li, Shuwang
AU - Song, Lingyu
N1 - Funding Information:
The research of WH has been supported by the American Heart Association under Grant 17SDG33660722 and the Institute for CyberScience Seed Grant. S. L. is partially supported by grant NSF ECCS-1307625 and NSF DMS-1720420 . SL thanks Emma Turian and John Lowengrub for technical discussions.
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2018/5/15
Y1 - 2018/5/15
N2 - Boundary integral method has been implemented successfully in practice for simulating problems with free boundaries. Though the method produces accurate and efficient numerical results, its convergence study is usually limited to numerical demonstrations by successively reducing time step and increasing resolution for a test problem. In this paper, we present a rigorous convergence and error analysis of the boundary integral method for a free boundary system. We focus our study on a nonlinear tumor growth problem. The boundary integral formulation yields a Fredholm type integral equation with moving boundaries. We show that in two dimensions, the convergence of the scheme in the L∞ norm has first order accuracy on the time direction and Δθα on the spatial direction.
AB - Boundary integral method has been implemented successfully in practice for simulating problems with free boundaries. Though the method produces accurate and efficient numerical results, its convergence study is usually limited to numerical demonstrations by successively reducing time step and increasing resolution for a test problem. In this paper, we present a rigorous convergence and error analysis of the boundary integral method for a free boundary system. We focus our study on a nonlinear tumor growth problem. The boundary integral formulation yields a Fredholm type integral equation with moving boundaries. We show that in two dimensions, the convergence of the scheme in the L∞ norm has first order accuracy on the time direction and Δθα on the spatial direction.
UR - http://www.scopus.com/inward/record.url?scp=85039150003&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85039150003&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2017.11.016
DO - 10.1016/j.cam.2017.11.016
M3 - Article
AN - SCOPUS:85039150003
VL - 334
SP - 128
EP - 157
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
ER -