Convergence analysis of moving finite element methods for space fractional differential equations

Most existent papers have focused on the fixed mesh methods for solving space fractional differential equations. However since some classes of space fractional differential equations may have singular or even finite-time blowup solutions, it is highly needed to develop adaptive mesh methods to solve these problems. In this paper the moving finite element methods are studied for a class of time-dependent space fractional differential equations. The convergence theories of the methods are derived with L2-norm and numerical examples are provided to support the theoretical results. To simplify the analysis, a fractional Ritz projection operator is introduced and the error estimation of the projection is derived under the moving mesh setting.