Praveen,
https://github.com/cpraveen/fembook/blob/master/deal.II/ex04/demo.cc
<https://nam01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgithub.com%2Fcpraveen%2Ffembook%2Fblob%2Fmaster%2Fdeal.II%2Fex04%2Fdemo.cc&data=02%7C01%7CWolfgang.Bangerth%40colostate.edu%7C64e1553a3ee443da7b0c08d8222ff1ad%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C637296936604213536&sdata=2KnxkD9r19uV5h41HYbakCAmD2PzuPddCZN0tv%2B%2BAE4%3D&reserved=0>
(Change quadrature rules in this code as indicated below)
degree=1
assembly using QGauss(2)
error computed using QGauss(2)
cells dofs L2 H1seminorm
1024 1089 1.606e-03 - 2.517e-01 -
4096 4225 4.015e-04 2.00 1.259e-01 1.00
16384 16641 1.004e-04 2.00 6.295e-02 1.00
65536 66049 2.510e-05 2.00 3.148e-02 1.00
262144 263169 6.275e-06 2.00 1.574e-02 1.00
We just observe the standard convergence rates, does not indicate
superconvergence.
The following two also yield standard convergence rates
degree=1
assembly using QGauss(2)
error computed using QGaussLobatto(2)
degree=1
assembly using QGaussLobatto(2)
error computed using QGaussLobatto(2)
This indicates there is no superconvergence at the mesh vertices.
(In all cases above, the matrix is exactly assembled.)
Interesting.
But then, was I completely wrong that something like superconvergence points
exist? Or does the concept only apply when we solve the Laplace equation (the
Poisson equation with f=0)? What is your recollection of superconvergence?
Best
W.
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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