19 November 2014 10:35:27 PM FEM1D_LAGRANGE_PRB C version. Test the FEM1D_LAGRANGE library. LEGENDRE_SET_TEST LEGENDRE_SET returns points and weights of Gauss-Legendre quadrature rules. N 1 X^4 Runge 1 2 0 2 2 2 0.222222 0.214286 3 2 0.4 0.958333 4 2 0.4 0.370927 5 2 0.4 0.706948 6 2 0.4 0.461701 7 2 0.4 0.616122 8 2 0.4 0.508122 9 2 0.4 0.578703 10 2 0.4 0.530372 LAGRANGE_VALUE_TEST LAGRANGE_VALUE evaluates the Lagrange basis polynomials. Lagrange basis points: 0: 0 1: 1 2: 2 3: 3 4: 4 I X L1(X) L2(X) L3(X) L4(X) L5(X) 0 0 1 0 -0 0 -0 1 0.5 0.273438 1.09375 -0.546875 0.21875 -0.0390625 2 1 -0 1 0 -0 0 3 1.5 -0.0390625 0.46875 0.703125 -0.15625 0.0234375 4 2 0 -0 1 0 -0 5 2.5 0.0234375 -0.15625 0.703125 0.46875 -0.0390625 6 3 -0 0 -0 1 0 7 3.5 -0.0390625 0.21875 -0.546875 1.09375 0.273438 8 4 0 -0 0 -0 1 LAGRANGE_DERIVATIVE_TEST LAGRANGE_DERIVATIVE evaluates the Lagrange basis derivative. Lagrange basis points: 0: 0 1: 1 2: 2 3: 3 4: 4 I X L1'(X) L2'(X) L3'(X) L4'(X) L5'(X) 0 0 -2.08333 4 -3 1.33333 -0.25 1 0.5 -0.916667 0.708333 0.375 -0.208333 0.0416667 2 1 -0.25 -0.833333 1.5 -0.5 0.0833333 3 1.5 0.0416667 -1.125 1.125 -0.0416667 0 4 2 0.0833333 -0.666667 0 0.666667 -0.0833333 5 2.5 0 0.0416667 -1.125 1.125 -0.0416667 6 3 -0.0833333 0.5 -1.5 0.833333 0.25 7 3.5 -0.0416667 0.208333 -0.375 -0.708333 0.916667 8 4 0.25 -1.33333 3 -4 2.08333 FEM1D_LAGRANGE_STIFFNESS_TEST FEM1D_LAGRANGE_STIFFNESS computes the stiffness matrix, the mass matrix, and right hand side vector for a finite element problem using Lagrange interpolation basis polynomials. Solving: -u''+u=x on 0 < x < 1 u(0) = u(1) = 0 Exact solution: u(x) = x - sinh(x)/sinh(1) Number of mesh points = 11 Number of quadrature points = 5 I X U U(exact) Error 0 0 -1.73472e-15 0 1.73472e-15 1 0.1 0.0956213 0.0147663 0.080855 2 0.2 0.227141 0.0286795 0.198462 3 0.3 0.25017 0.0408782 0.209292 4 0.4 0.406593 0.0504834 0.35611 5 0.5 0.5 0.0565906 0.443409 6 0.6 0.498838 0.0582599 0.440578 7 0.7 0.676584 0.0545074 0.622077 8 0.8 0.74956 0.0442945 0.705265 9 0.9 0.744763 0.0265183 0.718244 10 1 0 0 0 FEM1D_LAGRANGE_STIFFNESS_TEST FEM1D_LAGRANGE_STIFFNESS computes the stiffness matrix, the mass matrix, and right hand side vector for a finite element problem using Lagrange interpolation basis polynomials. Solving: -u''+u=x on 0 < x < 1 u(0) = u(1) = 0 Exact solution: u(x) = x - sinh(x)/sinh(1) Number of mesh points = 11 Number of quadrature points = 10 I X U U(exact) Error 0 0 -3.88578e-16 0 3.88578e-16 1 0.1 0.0147663 0.0147663 2.02616e-15 2 0.2 0.0286795 0.0286795 1.76803e-14 3 0.3 0.0408782 0.0408782 2.08167e-15 4 0.4 0.0504834 0.0504834 2.67286e-14 5 0.5 0.0565906 0.0565906 1.07692e-14 6 0.6 0.0582599 0.0582599 7.02216e-15 7 0.7 0.0545074 0.0545074 2.07265e-14 8 0.8 0.0442945 0.0442945 1.79717e-15 9 0.9 0.0265183 0.0265183 4.80171e-15 10 1 0 0 0 FEM1D_LAGRANGE_PRB Normal end of execution. 19 November 2014 10:35:27 PM