Dear Jean-Paul Now I understand why the heuristic method is less preferable and have a better sense of the least square method in this context.
Like a simple linear regression > <https://en.wikipedia.org/wiki/Linear_least_squares_(mathematics)>, the > least-squares method will minimise the error of your function (as given by > the quadrature data) projected onto the given finite element space (be it > continuous or discontinuous, low or high order, etc.). > Can I express this method as following: given the scalar data lower case p_j at the quadrature points, find the nodal values upper case P_i such that sum(p'_j - p_j)^2 is minimum where p'_j is the values at the quadrature points obtained by interpolating P_i ? I did not derive, instead learned from this link <https://books.google.com/books?id=8N18ew4LmIAC&pg=PA178&lpg=PA178&dq=quadrature+point+to+nodal+point+L2+projection&source=bl&ots=r51qRznCpd&sig=ykf8Y6-dLrWHUDOvtugJsVEE98U&hl=en&sa=X&ved=0ahUKEwjtzcGhwvLVAhWq7YMKHROvA8cQ6AEINDAC#v=onepage&q=quadrature%20point%20to%20nodal%20point%20L2%20projection&f=false>, that the least square method yields the following equation: MP = R where M is mass matrix, P is nodal values, and R is the volume integration of the scalar variable p. This involves solving additional linear equation but the equation itself is easy to assemble. Is my understanding right? Thank you so much Jie -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
