Abstract. The Petrov–Galerkin finite-element method with a lumped mass matrix is analyzed and it is stated that sometimes it causes an excessive smoothing of solutions and large errors. It is shown that weighting functions can be chosen so that the mentioned drawbacks are not practically manifested. The corresponding approximations are constructed in the form of systems of ordinary differential equations and finite-difference schemes. The theoretical results obtained are confirmed by calculation data.
Keywords: finite-element method, Petrov–Galerkin method, convection–diffusion equation, lumped approximations, artificial dissipation and dispersion.
Сирик Сергей Валентинович,
аспирант Национального технического университета Украины «Киевский политехнический институт»,
e-mail: accandar@gmail.com.