Error estimates of a FEM with lumping for parabolic PDEs
The paper is devoted to error estimates of a special FEM with lumping for parabolic PDEs in the L-2-norm. This well-known FEM is given by the use of the vertical line method and conforming linear finite elements on a triangulation. The main result of the paper are new estimates in the L-2-norm for the additional error term originated by lumping. Using these ones, for the FEM with lumping we can apply directly the proof technique of error estimates known for conforming FEMs.
lumping vertical line method parabolic problem finite element method