Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902141 | Journal of Computational and Applied Mathematics | 2018 | 46 Pages |
Abstract
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 Lâ norm has first order accuracy on the time direction and Îθα on the spatial direction.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Wenrui Hao, Bei Hu, Shuwang Li, Lingyu Song,