Virtual element method for the Sobolev equations

The virtual element method for the Sobolev equations is proposed in this paper, where the semi-discrete scheme and the fully discrete scheme are both discussed. With the help of the energy projection operator defined by the discrete bilinear form, the corresponding optimal error estimates in the L2$$ {L}<^>2 $$ norm and H1$$ {H}<^>1 $$ semi-norm for both the semi-discrete solution and the fully discrete solution are deduced. Finally, three numerical examples are carried out to verify the theoretical results.