l2error.hh

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#ifndef DUMUX_TEST_L2_ERROR_HH
#define DUMUX_TEST_L2_ERROR_HH
 
#include <vector>
#include <cmath>
 
namespace Dumux {
 
template<class Scalar, class ModelTraits, class PrimaryVariables>
class NavierStokesTestL2Error
{
    using Indices = typename ModelTraits::Indices;
 
public:
 
    template<class Problem, class SolutionVector>
    static auto calculateL2Error(const Problem& problem, const SolutionVector& curSol)
    {
        using GridGeometry = std::decay_t<decltype(problem.gridGeometry())>;
        PrimaryVariables sumError(0.0), sumReference(0.0), l2NormAbs(0.0), l2NormRel(0.0);
 
        const int numFaceDofs = problem.gridGeometry().numFaceDofs();
 
        std::vector<Scalar> staggeredVolume(numFaceDofs);
        std::vector<Scalar> errorVelocity(numFaceDofs);
        std::vector<Scalar> velocityReference(numFaceDofs);
        std::vector<int> directionIndex(numFaceDofs);
 
        Scalar totalVolume = 0.0;
 
        for (const auto& element : elements(problem.gridGeometry().gridView()))
        {
            auto fvGeometry = localView(problem.gridGeometry());
            fvGeometry.bindElement(element);
 
            for (auto&& scv : scvs(fvGeometry))
            {
                // treat cell-center dofs
                const auto dofIdxCellCenter = scv.dofIndex();
                const auto& posCellCenter = scv.dofPosition();
                const auto analyticalSolutionCellCenter = problem.dirichletAtPos(posCellCenter)[Indices::pressureIdx];
                const auto numericalSolutionCellCenter = curSol[GridGeometry::cellCenterIdx()][dofIdxCellCenter][Indices::pressureIdx - ModelTraits::dim()];
                sumError[Indices::pressureIdx] += squaredDiff_(analyticalSolutionCellCenter, numericalSolutionCellCenter) * scv.volume();
                sumReference[Indices::pressureIdx] += analyticalSolutionCellCenter * analyticalSolutionCellCenter * scv.volume();
                totalVolume += scv.volume();
 
                // treat face dofs
                for (auto&& scvf : scvfs(fvGeometry))
                {
                    const int dofIdxFace = scvf.dofIndex();
                    const int dirIdx = scvf.directionIndex();
                    const auto analyticalSolutionFace = problem.dirichletAtPos(scvf.center())[Indices::velocity(dirIdx)];
                    const auto numericalSolutionFace = curSol[GridGeometry::faceIdx()][dofIdxFace][0];
                    directionIndex[dofIdxFace] = dirIdx;
                    errorVelocity[dofIdxFace] = squaredDiff_(analyticalSolutionFace, numericalSolutionFace);
                    velocityReference[dofIdxFace] = squaredDiff_(analyticalSolutionFace, 0.0);
                    const Scalar staggeredHalfVolume = 0.5 * scv.volume();
                    staggeredVolume[dofIdxFace] = staggeredVolume[dofIdxFace] + staggeredHalfVolume;
                }
            }
        }
 
        // get the absolute and relative discrete L2-error for cell-center dofs
        l2NormAbs[Indices::pressureIdx] = std::sqrt(sumError[Indices::pressureIdx] / totalVolume);
        l2NormRel[Indices::pressureIdx] = std::sqrt(sumError[Indices::pressureIdx] / sumReference[Indices::pressureIdx]);
 
        // get the absolute and relative discrete L2-error for face dofs
        for(int i = 0; i < numFaceDofs; ++i)
        {
            const int dirIdx = directionIndex[i];
            const auto error = errorVelocity[i];
            const auto ref = velocityReference[i];
            const auto volume = staggeredVolume[i];
            sumError[Indices::velocity(dirIdx)] += error * volume;
            sumReference[Indices::velocity(dirIdx)] += ref * volume;
        }
 
        for(int dirIdx = 0; dirIdx < ModelTraits::dim(); ++dirIdx)
        {
            l2NormAbs[Indices::velocity(dirIdx)] = std::sqrt(sumError[Indices::velocity(dirIdx)] / totalVolume);
            l2NormRel[Indices::velocity(dirIdx)] = std::sqrt(sumError[Indices::velocity(dirIdx)] / sumReference[Indices::velocity(dirIdx)]);
        }
        return std::make_pair(l2NormAbs, l2NormRel);
    }
 
private:
 
    template<class T>
    static T squaredDiff_(const T& a, const T& b)
    {
        return (a-b)*(a-b);
    }
 
};
} // end namespace Dumux
 
#endif