17 September 2021 9:31:12.450 AM FEM1D_LAGRANGE_TEST FORTRAN90 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 2.00000 0.00000 2.00000 2 2.00000 0.222222 0.214286 3 2.00000 0.400000 0.958333 4 2.00000 0.400000 0.370927 5 2.00000 0.400000 0.706948 6 2.00000 0.400000 0.461701 7 2.00000 0.400000 0.616122 8 2.00000 0.400000 0.508122 9 2.00000 0.400000 0.578703 10 2.00000 0.400000 0.530372 LAGRANGE_VALUE_TEST LAGRANGE_VALUE evaluates the Lagrange basis polynomials. Lagrange basis points: 1: 0.0000000 2: 1.0000000 3: 2.0000000 4: 3.0000000 5: 4.0000000 I X L1(X) L2(X) L3(X) L4(X) L5(X) 1 0.0000 1.0000 0.0000 -0.0000 0.0000 -0.0000 2 0.5000 0.2734 1.0938 -0.5469 0.2188 -0.0391 3 1.0000 -0.0000 1.0000 0.0000 -0.0000 0.0000 4 1.5000 -0.0391 0.4688 0.7031 -0.1562 0.0234 5 2.0000 0.0000 -0.0000 1.0000 0.0000 -0.0000 6 2.5000 0.0234 -0.1562 0.7031 0.4688 -0.0391 7 3.0000 -0.0000 0.0000 -0.0000 1.0000 0.0000 8 3.5000 -0.0391 0.2188 -0.5469 1.0938 0.2734 9 4.0000 0.0000 -0.0000 0.0000 -0.0000 1.0000 LAGRANGE_DERIVATIVE_TEST LAGRANGE_DERIVATIVE evaluates the Lagrange basis derivative. Lagrange basis points: 1: 0.0000000 2: 1.0000000 3: 2.0000000 4: 3.0000000 5: 4.0000000 I X L1'(X) L2'(X) L3'(X) L4'(X) L5'(X) 1 0.0000 -2.0833 4.0000 -3.0000 1.3333 -0.2500 2 0.5000 -0.9167 0.7083 0.3750 -0.2083 0.0417 3 1.0000 -0.2500 -0.8333 1.5000 -0.5000 0.0833 4 1.5000 0.0417 -1.1250 1.1250 -0.0417 0.0000 5 2.0000 0.0833 -0.6667 0.0000 0.6667 -0.0833 6 2.5000 0.0000 0.0417 -1.1250 1.1250 -0.0417 7 3.0000 -0.0833 0.5000 -1.5000 0.8333 0.2500 8 3.5000 -0.0417 0.2083 -0.3750 -0.7083 0.9167 9 4.0000 0.2500 -1.3333 3.0000 -4.0000 2.0833 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 1 0.0000 0.444089E-15 0.00000 0.444089E-15 2 0.1000 0.956213E-01 0.147663E-01 0.808550E-01 3 0.2000 0.227141 0.286795E-01 0.198462 4 0.3000 0.250170 0.408782E-01 0.209292 5 0.4000 0.406593 0.504834E-01 0.356110 6 0.5000 0.500000 0.565906E-01 0.443409 7 0.6000 0.498838 0.582599E-01 0.440578 8 0.7000 0.676584 0.545074E-01 0.622077 9 0.8000 0.749560 0.442945E-01 0.705265 10 0.9000 0.744763 0.265183E-01 0.718244 11 1.0000 0.00000 0.00000 0.00000 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 1 0.0000 0.471845E-15 0.00000 0.471845E-15 2 0.1000 0.147663E-01 0.147663E-01 0.249800E-14 3 0.2000 0.286795E-01 0.286795E-01 0.178746E-13 4 0.3000 0.408782E-01 0.408782E-01 0.205391E-14 5 0.4000 0.504834E-01 0.504834E-01 0.267286E-13 6 0.5000 0.565906E-01 0.565906E-01 0.107692E-13 7 0.6000 0.582599E-01 0.582599E-01 0.702216E-14 8 0.7000 0.545074E-01 0.545074E-01 0.206155E-13 9 0.8000 0.442945E-01 0.442945E-01 0.179717E-14 10 0.9000 0.265183E-01 0.265183E-01 0.480171E-14 11 1.0000 0.00000 0.00000 0.00000 FEM1D_LAGRANGE_TEST Normal end of execution. 17 September 2021 9:31:12.451 AM