LAUSR

ABSTRACT This article deals with the development of the virtual element method for the approximation of semilinear hyperbolic problems. For the space discretization, two different operators are used: the energy projection operator and an internal -projection operator . In order to deal with the time derivative, a Newmark scheme is employed; and the resulted fully discrete scheme is analysed. Moreover, with the help of projection operators, optimal error estimates are derived for both semi- and fully discrete schemes in -norm and -norm. We have conducted numerical experiments on polygonal meshes to illustrate the performance of the proposed scheme and validate the theoretical findings.