Alternating Direction Finite Element Method for a Class of Moving Boundary Problems

摘要

An alternating direction finite element scheme for a class of moving boundary problems is studied. Using coordinate transformations of the spatial variants, a new domain independent of the time is obtained and an ADFE scheme on the new domain is proposed. Then the unique solvability of the approximation scheme is proved, and optimal H~1 and L~2 norm space estimates and O((Δt)~2) estimate for the temporal variant are obtained.