Could we calculate the errors in H1 norm for Poisson example in tutorial?

[Thomas]

Could we calculate the errors in H1 norm for Poisson example? For example, global error or local error in H1 norm. Thank you.

[Lukasz Kaczmraczyk]

Hello Thomas,

In Poisson tutorial, http://mofem.eng.gla.ac.uk/mofem/html/poisson_tut1.html, error is calculated in H1 norm. Calculation of error is implemented in file http://mofem.eng.gla.ac.uk/mofem/html/_poisson_operators_8hpp-example.html, see operator OpError, in particular http://mofem.eng.gla.ac.uk/mofem/html/struct_poisson_example_1_1_op_error.html.

You can notice there in method PoissonExample::OpError::iNtegrate(), that both error on functions values and functions gradients is integrated.

      for(int gg = 0;gg!=nbIntegrationPts;gg++) {
        double alpha = vol*t_w;
        // evalue exact value
        double exact_u = uValue(t_coords(NX),t_coords(NY),t_coords(NZ));
        // evalue exact hradient
        t_exact_grad = gValue(t_coords(NX),t_coords(NY),t_coords(NZ));
        // calculate gradient errro
        t_error_grad(i) = t_grad(i)-t_exact_grad(i);
        // error
        double error = pow(t_u-exact_u,2)+t_error_grad(i)*t_error_grad(i);
        // iterate over base functions
        data.getFieldData()[0] += alpha*error;
        ++t_w;      // move to next integration point
        ++t_u;      // next value of function at integration point
        ++t_grad;   // next gradient at integration point
        ++t_coords; // next coordinate at integration point
      }

Regards,

Lukasz