17 September 2021 9:31:13.803 AM FEM2D_HEAT_RECTANGLE FORTRAN90 version: Solution of the time dependent heat equation on a unit box in 2 dimensions. Ut - Uxx - Uyy = F(x,y,t) in the box U(x,y,t) = G(x,y,t) for (x,y) on the boundary. U(x,y,t) = H(x,y,t) for t = T_INIT. The finite element method is used, with piecewise quadratic basis functions on 6 node triangular elements. The backward Euler formula is used for the time derivative. The corner nodes of the triangles are generated by an underlying grid whose dimensions are NX = 5 NY = 5 Number of nodes = 81 Number of elements = 32 The matrix half bandwidth is 18 The matrix row size is 55 FEM2D_HEAT_RECTANGLE: Wrote an EPS file "nodes.eps" containing a picture of the nodes. FEM2D_HEAT_RECTANGLE: Wrote an ASCII node file "nodes.txt" of the form X(I), Y(I) which can be used for plotting. FEM2D_HEAT_RECTANGLE: Wrote an EPS file "elements.eps" containing a picture of the elements. FEM2D_HEAT_RECTANGLE: Wrote an ASCII element file "elements.txt" of the form Node(1) Node(2) Node(3) Node(4) Node(5) Node(6) which can be used for plotting. Initial time = 0.00000 Final time = 0.500000 Step size = 0.500000E-01 Number of steps = 10 Time L2 Error H1 Error 0.500000E-01 0.423576E-02 0.128476 0.100000 0.401111E-02 0.122263 0.150000 0.380908E-02 0.116322 0.200000 0.362096E-02 0.110660 0.250000 0.344343E-02 0.105269 0.300000 0.327508E-02 0.100137 0.350000 0.311516E-02 0.952552E-01 0.400000 0.296314E-02 0.906103E-01 0.450000 0.281859E-02 0.861916E-01 0.500000 0.268110E-02 0.819881E-01 FEM2D_HEAT_RECTANGLE: Normal end of execution. 17 September 2021 9:31:13.812 AM