l2norm.hh

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#ifndef DUMUX_TEST_L2_NORM_HH
#define DUMUX_TEST_L2_NORM_HH
 
#include <cmath>
#include <type_traits>
#include <dune/geometry/quadraturerules.hh>
#include <dumux/common/parameters.hh>
#include <dumux/discretization/elementsolution.hh>
#include <dumux/discretization/evalsolution.hh>
 
namespace Dumux {
 
template<class Scalar>
struct L2Norm
{
    template<class Problem, class Solution>
    static Scalar computeErrorNorm(const Problem &problem, const Solution& sol, int order)
    {
        // calculate the L2-Norm and hmax
        Scalar norm = 0.0;
 
        // iterate over all elements
        const auto& gg = problem.gridGeometry();
        for (const auto& element : elements(gg.gridView()))
        {
            const auto geometry = element.geometry();
            const auto center = geometry.center();
            const auto elemSol = elementSolution(element, sol, gg);
 
            // maybe exclude some elements from the norm
            static const bool excludeInnerBulk = getParam<bool>("Problem.NormExcludeInnerBulk");
            static const Scalar radius = getParam<Scalar>("SpatialParams.Radius") + 0.01;
            using GridView = std::decay_t<decltype(gg.gridView())>;
            if (int(GridView::dimension) == 3 && excludeInnerBulk && std::sqrt(center[0]*center[0] + center[1]*center[1]) < radius)
                continue;
 
            const auto& quad = Dune::QuadratureRules<Scalar, GridView::dimension>::rule(geometry.type(), order);
            for(auto&& qp : quad)
            {
                const auto globalPos = geometry.global(qp.position());
                const Scalar pe = problem.exactSolution(globalPos);
                const Scalar p = evalSolution(element, geometry, gg, elemSol, globalPos)[0];
                norm += (p - pe)*(p - pe)*qp.weight()*geometry.integrationElement(qp.position());
            }
        }
 
        return std::sqrt(norm);
    }
 
    template<class Problem>
    static Scalar computeNormalization(const Problem &problem, int order)
    {
        // calculate the L2-Norm of the exact solution vector
        Scalar norm = 0.0;
 
        // iterate over all elements
        const auto& gg = problem.gridGeometry();
        for (const auto& element : elements(gg.gridView()))
        {
            const auto geometry = element.geometry();
            const auto center = geometry.center();
 
            // maybe exclude some elements from the norm
            static const bool excludeInnerBulk = getParam<bool>("Problem.NormExcludeInnerBulk");
            static const Scalar radius = getParam<Scalar>("SpatialParams.Radius") + 0.01;
            using GridView = std::decay_t<decltype(gg.gridView())>;
            if (int(GridView::dimension) == 3 && excludeInnerBulk && std::sqrt(center[0]*center[0] + center[1]*center[1]) < radius)
                continue;
 
            const auto& quad = Dune::QuadratureRules<Scalar, GridView::dimension>::rule(geometry.type(), order);
            for(auto&& qp : quad)
            {
                const auto globalPos = geometry.global(qp.position());
                const Scalar pe = problem.exactSolution(globalPos);
                norm += pe*pe*qp.weight()*geometry.integrationElement(qp.position());
            }
        }
 
        return std::sqrt(norm);
    }
};
 
} // end namespace Dumux
 
#endif