Comoving mesh method for certain classes of moving boundary problems

A Lagrangian-type numerical scheme called the "comoving mesh method" or CMM is developed for numerically solving certain classes of moving boundary problems which include, example, classical Hele-Shaw flow problem and well-known mean curvature problem. This finite element exploits idea that normal velocity field can be extended throughout entire domain definition using, instance, Laplace operator. Then, as well are easily updated at every time step by nodal points along this field. The feasibility method, highlighting its practicality, illustrated through various experiments. Also, in order to examine accuracy proposed scheme, experimental convergences between manufactured solutions these examples also calculated.