  Finite element methods for symmetric linear hyperbolic systems using
unstructured advancing fronts (satisfying a causality condition) are considered
in this work. Convergence results and error bounds are obtained for mapped tent
pitching schemes made with standard discontinuous Galerkin discretizations for
spatial approximation on mapped tents. Techniques to study semidiscretization
on mapped tents, design fully discrete schemes, prove local error bounds, prove
stability on spacetime fronts, and bound error propagated through unstructured
layers are developed.
