> I don't think that's true, non-planar faces are not as easy as general > bricks in 3D. I tried that some time ago, but neither maple nor myself > were able to find an explicit expression for the measure of a general > quadrilateral face. We could use some numerical quadrature formula, > though. That's what we usually do now.
True. I believe that the term that needs to be integrated is a rational expression involving the reference coordinates xi,eta of the reference face, and both numerator and denominator of the expression should be a polynomial of degree 2. You may well be right that that can't be integrated analytically. If you do numerical quadrature using the trapezoidal rule, for example, you may want to use the GeometryInfo::alternating_form_at_vertices function to compute the determinant of the Jacobian matrix at the vertices. Best W. ------------------------------------------------------------------------- Wolfgang Bangerth email: [email protected] www: http://www.math.tamu.edu/~bangerth/ _______________________________________________ dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii
