The Newmark Method and a Space-Time FEM for the Second-Order Wave Equation

摘要

For the second-order wave equation, we compare the Newmark Galerkin method with a stabilised space-time finite element method for tensor-product space-time discretisations with piecewise multilinear, continuous ansatz and test functions leading to an unconditionally stable Galerkin-Petrov scheme, which satisfies a space-time error estimate. We show that both methods require to solve a linear system with the same system matrix. In particular, the stabilised space-time finite element method can be solved sequentially in time as the Newmark Galerkin method. However, the treatment of the right-hand side of the wave equation is different, where the Newmark Galerkin method requires more regularity.