Given that some of the mass lumping techniques, for example, row-sum lumping does not produce practically viable lumped mass matrices for all the element shapes, what are the techniques used for mass lumping for higher-order elements? I am particularly interested in applications in CFD.
I know that deal.ii has a tutorial on the projection method where the diffusion term is treated implicity. So, mass lumping is not necessary here. FreeFem uses explicit step for the diffusion term but demonstrates the implementation with P1 elements only.
Are there any libraries that solve the diffusion term explicitly using lumped-mass matrices for the velocity field when LBB-stable combinations using higher-order elements are employed?
I would appreciate any useful references on the topic. Thanks in advance.