In this work we analyse the 1D strongly damped wave equation from the analytical and numerical point of view. This equation arises from the equation of motion of the string pendulum in the vertical position. An approach to solve the equation numerically by using the finite elements in space and time is presented. This employs the discontinuous Galerkin (dG(q), q=0,1) or continuous Galerkin method in time and piecewise linear or Hermite cubic elements in space. The advantages and difficulties of the proposed discretisation methods are discussed. We also prove the existence and uniquence of the continuous as well as the discrete solution.
The main focus is on ways to estimate the quantity of interest such are the error in the energy norm and the dissipative term, by use of the energy, dual and goal-oriented techniques. Most of the derived results are verified on examples.