Finite element solution of a hyperbolic-parabolic problem (Q1340775)

This is a detailed and careful study of the numerical analysis (that is here: without numerical experiences) of initial-boundary value problems for linear parabolic or hyperbolic equations, using time discretizations through the Rothe method (Euler's backward formula) and finite element approximation for the remaining at each time-stage two-dimensional elliptic boundary value problems (with Dirichlet and Neumann conditions on certain sectors of the boundary). Existence and uniqueness of the solution and the convergence of the combined method in suitably chosen function spaces are proved.