Fix a bug for the integration on triangles

src/analysis/PolynomialP.hpp

@@ -614,7 +614,7 @@ integrate(const PolynomialP<N, Dimension> Q, const std::array<TinyVector<Dimensi
       for (size_t i = 1; i < weight_list.size(); ++i) {
         value += weight_list[i] * Q(t(point_list[i]));
       }
-      integral = value;
+      integral = t.jacobianDeterminant() * value;
     } else {
       const QuadratureFormula<2>& lN = QuadratureManager::instance().getSquareFormula(GaussQuadratureDescriptor(N));
       auto point_list                = lN.pointList();

src/analysis/TaylorPolynomial.hpp

@@ -641,7 +641,7 @@ integrate(const TaylorPolynomial<N, Dimension> Q, const std::array<TinyVector<Di
       for (size_t i = 1; i < weight_list.size(); ++i) {
         value += weight_list[i] * Q(t(point_list[i]));
       }
-      integral = value;
+      integral = t.jacobianDeterminant() * value;
     } else {
       const QuadratureFormula<2>& lN = QuadratureManager::instance().getSquareFormula(GaussQuadratureDescriptor(N));
       auto point_list                = lN.pointList();

tests/test_PolynomialP.cpp

@@ -189,6 +189,7 @@ TEST_CASE("PolynomialP", "[analysis]")
     for (size_t i = 1; i < weight_list2.size(); ++i) {
       value2 += weight_list2[i] * p1(t(point_list2[i]));
     }
+    value2 *= t.jacobianDeterminant();
     const QuadratureFormula<1>& l1 = QuadratureManager::instance().getLineFormula(GaussQuadratureDescriptor(2));
     const LineTransformation<2> u{positions4[0], positions4[1]};
     double value4 = 0.;

tests/test_TaylorPolynomial.cpp

@@ -199,6 +199,7 @@ TEST_CASE("TaylorPolynomial", "[analysis]")
     for (size_t i = 1; i < weight_list2.size(); ++i) {
       value2 += weight_list2[i] * p1(t(point_list2[i]));
     }
+    value2 *= t.jacobianDeterminant();
     const QuadratureFormula<1>& l1 = QuadratureManager::instance().getLineFormula(GaussQuadratureDescriptor(2));
     const LineTransformation<2> u{positions4[0], positions4[1]};
     double value4 = 0.;