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

摘要

This is a study of certain finite element methods designed forconvection-dominated, time-dependent partial differential equations.Specifically, we analyze high order space-time tensor product finite elementdiscretizations, used in a method of lines approach coupled with meshmodification to solve linear partial differential equations. Mesh modificationcan be both continuous (moving meshes) and discrete (static rezone). Thesemethods can lead to significant savings in computation costs for problemshaving solutions that develop steep moving fronts or other localizedtime-dependent features of interest. Our main result is a symmetric a priorierror estimate for the finite element solution computed in this setting.