We present a unified analysis of finite element methods for problems with prescribed moving boundaries. In particular, we study an abstract parabolic problem posed on a moving domain with prescribed evolution, discretized in space with a finite element space that is associated with a moving mesh that conforms to the domain at all times. The moving mesh is assumed to evolve smoothly in time, exc...

In this dissertation a moving mesh method finite element method is used to approximate moving boundary solutions to the shallow water equations. An Arbitrary Lagrangian Eulerian method is applied to an existing finite element scheme. Some exact solutions to the shallow water equations in a parabolic basin are shown for comparison. An investigation is conducted into the accuracy of the method. I...

In this paper, transverse and longitudinal vibration of nonlinear plate under exciting of orbiting mass is considered based on first-order shear deformation theory. The nonlinear governing equation of motion are discretized by the finite element method in combination with Newmark’s time integration scheme under von Karman strain-displacement assumptions. For validation of method and formulation...

The non-equilibrium Richards equation is solved using a moving finite element method in this paper. The governing equation is discretized spatially with a standard finite element method, and temporally with second-order Runge-Kutta schemes. A strategy of the mesh movement is based on the work by Li et al. [R. Li, T. Tang and P. W. Zhang, A moving mesh finite element algorithm for singular probl...

this paper was concerned with studying the magnetohydrodynamic steady laminar free convection flow of a micropolar fluid past a continuously moving surface in the presence of heat generation and thermal radiation. similarity transformation was employed to transform the governing partial differential equations into ordinary ones, which were then solved numerically using the finite element method...