  Variational time discretization schemes are getting of increasing importance
for the accurate numerical approximation of transient phenomena. The
applicability and value of mixed finite element methods (MFEM) in space for
simulating transport processes have been demonstrated in a wide class of works.
We consider a family of continuous Galerkin-Petrov time discretization schemes
that is combined with a mixed finite element (MFE) approximation of the spatial
variables. The existence and uniqueness of the semidiscrete approximation and
of the fully discrete solution are established. For this, the
Banach-Ne\v{c}as-Babu\v{s}ka theorem is applied in a non-standard way. Error
estimates with explicit rates of convergence are proved for the scalar and
vector-valued variable. An optimal order estimate in space and time is proved
by duality techniques for the scalar variable. The convergence rates are
analyzed and illustrated by numerical experiments, also on stochastically
perturbed meshes.

Numerical Analysis