On 5/21/21 1:52 PM, Shahin Heydari wrote:
m_i = sigma (m_ij) = int(phi_i dx)

Right. You compute the integral as a sum over the integrals on each cell. So when you do

  for (cell = ...)
    for (i=...)
      {
        lump = 0;
        for (q=...)
          lump += ...

        lump_cell_matrix(i,i) = lump;
      }

then this is correct if you then add lump_cell_matrix(i,i) to your global 
matrix.

You mention in your original question that you are unsure about what to do with Q2 (or higher) elements. This is a difficult question, but there is a good amount of literature on the topic. Just search for "mass lumping higher order elements".

Best
 W.

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Wolfgang Bangerth          email:                 [email protected]
                           www: http://www.math.colostate.edu/~bangerth/

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