An Error Analysis of Some Higher Order Space-Time Moving Finite Elements

Abstract: This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a method of lines approach coupled with mesh modification to solve linear partial differential equations. Mesh modification can be both continuous (moving meshes) and discrete (static rezone). These methods can lead to significant savings in computation costs for problems having solutions that develop steep moving fronts or other localized time-dependent features of interest. Our main result is a symmetric a priori error estimate for the finite element solution computed in this setting.