@article{oai:kanazawa-u.repo.nii.ac.jp:00011120,
 author = {赤川, 佳穂 and Faizal, Makhrus and Akagawa, Yoshiho and Alvi, Syahrini},
 journal = {The science reports of the Kanazawa University = 金沢大学理科報告},
 month = {Jan},
 note = {We study a 1-D hyperbolic-type problem with free boundary which describes the motion of a piece of tape being peeled off from a surface. The graph of the solution represents the shape of the tape, which displays contact angle dynamics at the free bound-ary (the location of peeling). The contact angle dynamics lead to singularities located on the free boundary, which cause a slight difficulty. Under some assumptions, this problem can be solved numerically by a so-called fixed domain method. This method is a numer-ical method which transforms the domain of the positive part of the solution into a fixed domain using a change of variables and solves the problem in that domain. Although this method has a high accuracy, it can not be applied in some cases. Hence other numer-ical methods are chosen for solving a regularized problem, i.e., the singularities on the free boundary are regularized by a smoothing function. The numerical methods are: two types of finite difference methods, the finite element method and discrete Morse flow. In this paper, the error of solving the regularized problem instead of the original problem is calculated. Since the choice of the parameter for smoothing function is important for the accuracy, we propose a formula to estimate the optimal parameter in order to mini-mize the error. This formula is verified by numerical experiments and we find that it can estimate the optimal parameter. In addition, based on comparisons between the numeri-cal methods, we find that the finite difference methods have better performance than the other methods.},
 pages = {27--50},
 title = {Numerical methods for 1-D hyperbolic-type problems with free boundary},
 volume = {59},
 year = {2015}
}