Galerkin-Type Approximations which are Discontinuous in Time for Parabolic Equations in a Variable Domain

General linear parabolic equations are considered in a given time dependent domain and a general class of Galerkin-type approximations is considered which are continuous with respect to the space variables, but which admit discontinuities with respect to time at each time step. Unconditional stability is proved and a general error estimate is established. These results are applied to certain finite element methods based on space-time finite elements.