I am trying to debug a SUPG FEM code for flow problems (based on Brooks Hughes 1982) and have a question about the Lumped Mass Matrix. My understanding of the Lumped Mass Matrix is that for any given element the mass of that element is simply distributed evenly over the number of nodes.(adsbygoogle = window.adsbygoogle || []).push({});

In my case I am using P2P1 tetrahedral elements which, in the case of an element on the no slip boundary, results in a 60% loss of mass at the local level because of the 6 velocity nodes (3 vertex and 3 edge nodes) that would lie on the no slip surface. The reason for this is that nodes on the boundary represent known velocity values and are not required in the global system of equations. This ulimately results in the sum of my diagonal entries in the global Lumped Mass Matrix not being equal to the mass of fluid in my system.

My question is: For an element on the no slip boundary, should additional mass be lumped at those unknown nodes such that the total mass of the fluid in my computational domain is equal to the sum of diagonal entries in the global Lumped Mass Matrix?

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# FEM: Local lumped mass matrices for elements on no slip boundaries.

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