A Continuation Problem for Computing Solutions of Discretised Evolution Problems with Application to Plane Quasi-Static Contact Problems with Friction

International audienceA continuation problem for finding successive solutions of discretised abstract first-order evolution problems is proposed and a general piecewise $C^{1}$ continuation problem is studied. A condition ensuring local existence and uniqueness of its solution curves is given. An analogy of the first-order system of smooth problems is derived and results of existence and uniqueness of its solutions are stated. Possibility of continuation of a solution curve along directions solving the first-order system is discussed. A technique for numerical continuation of the solution curves is developed. Furthermore, an application of the abstract continuation problem is presented for plane quasi-static contact problems with friction. Various formulations of the first-order system are derived for this case so that the analysis from the abstract frame can be developed and supplemented. Finally, the proposed numerical continuation is tested