fem_check22_la.adb running solve uxx(x,y) + 2 uxy(x,y) + 3 uyy(x,y) + 4 ux(x,y) + 5 uy(x,y) + 6 u(x,y) = c(x,y) boundary conditions computed using u(x) analytic solution may be given by u(x) = x^3 + y^3 + xy + 1 Gauss-Legendre integration used xmin= 0.00, xmax= 1.00, ymin= 0.00, ymax= 1.00 nx= 4, ny= 4 x grid and analytic solution at ymin i= 1, Ua( 0.00000, 0.00000)= 1.00000 i= 2, Ua( 0.33333, 0.00000)= 1.03704 i= 3, Ua( 0.66667, 0.00000)= 1.29630 i= 4, Ua( 1.00000, 0.00000)= 2.00000 y grid and analytic solution at xmin ii= 1, Ua( 0.00000, 0.00000)= 1.00000 ii= 2, Ua( 0.00000, 0.33333)= 1.03704 ii= 3, Ua( 0.00000, 0.66667)= 1.29630 ii= 4, Ua( 0.00000, 1.00000)= 2.00000 solution at i= 1, x= 0.000, ii= 1, y= 0.000 is 1.000 solution at i= 1, x= 0.000, ii= 2, y= 0.333 is 1.037 solution at i= 1, x= 0.000, ii= 3, y= 0.667 is 1.296 solution at i= 1, x= 0.000, ii= 4, y= 1.000 is 2.000 solution at i= 2, x= 0.333, ii= 1, y= 0.000 is 1.037 solution at i= 2, x= 0.333, ii= 2, y= 0.333 is 1.185 solution at i= 2, x= 0.333, ii= 3, y= 0.667 is 1.556 solution at i= 2, x= 0.333, ii= 4, y= 1.000 is 2.370 solution at i= 3, x= 0.667, ii= 1, y= 0.000 is 1.296 solution at i= 3, x= 0.667, ii= 2, y= 0.333 is 1.556 solution at i= 3, x= 0.667, ii= 3, y= 0.667 is 2.037 solution at i= 3, x= 0.667, ii= 4, y= 1.000 is 2.963 solution at i= 4, x= 1.000, ii= 1, y= 0.000 is 2.000 solution at i= 4, x= 1.000, ii= 2, y= 0.333 is 2.370 solution at i= 4, x= 1.000, ii= 3, y= 0.667 is 2.963 solution at i= 4, x= 1.000, ii= 4, y= 1.000 is 4.000 boundary i= 1, x= 0.000, ii= 1, y= 0.000 is 1.00000000000000E+00 boundary i= 1, x= 0.000, ii= 4, y= 1.000 is 2.00000000000000E+00 boundary i= 2, x= 0.333, ii= 1, y= 0.000 is 1.03703703703704E+00 boundary i= 2, x= 0.333, ii= 4, y= 1.000 is 2.37037037037037E+00 boundary i= 3, x= 0.667, ii= 1, y= 0.000 is 1.29629629629630E+00 boundary i= 3, x= 0.667, ii= 4, y= 1.000 is 2.96296296296296E+00 boundary i= 4, x= 1.000, ii= 1, y= 0.000 is 2.00000000000000E+00 boundary i= 4, x= 1.000, ii= 4, y= 1.000 is 4.00000000000000E+00 boundary i= 1, x= 0.000, ii= 1, y= 0.000 is 1.00000000000000E+00 boundary i= 4, x= 1.000, ii= 1, y= 0.000 is 2.00000000000000E+00 boundary i= 1, x= 0.000, ii= 2, y= 0.333 is 1.03703703703704E+00 boundary i= 4, x= 1.000, ii= 2, y= 0.333 is 2.37037037037037E+00 boundary i= 1, x= 0.000, ii= 3, y= 0.667 is 1.29629629629630E+00 boundary i= 4, x= 1.000, ii= 3, y= 0.667 is 2.96296296296296E+00 boundary i= 1, x= 0.000, ii= 4, y= 1.000 is 2.00000000000000E+00 boundary i= 4, x= 1.000, ii= 4, y= 1.000 is 4.00000000000000E+00 calling gaulegf npx= 12 calling gaulegf npy= 12 xx(1)= 9.21968287664038E-03, xx(2)= 4.79413718147626E-02, wx(1)= 2.35876681932542E-02, wx(2)= 5.34696629976591E-02 yy(1)= 9.21968287664038E-03, yy(2)= 4.79413718147626E-02, wy(1)= 2.35876681932542E-02, wy(2)= 5.34696629976591E-02 galk(xx(2),yy(2))= 8.45582953189805E+00 galf(xx(2),yy(2))= 1.40395847414887E+00 compute stiffness matrix Legendre integration= 1.77201849489795E+00, at i= 2, j= 1, ii= 2, jj= 1 Legendre integration=-1.04969387755102E+00, at i= 2, j= 1, ii= 2, jj= 2 Legendre integration= 6.06983418367310E-02, at i= 2, j= 1, ii= 2, jj= 3 Legendre integration= 5.26913265306129E-02, at i= 2, j= 1, ii= 2, jj= 4 Legendre integration=-6.25522959183671E-01, at i= 2, j= 1, ii= 3, jj= 1 Legendre integration= 2.34967155612244E+00, at i= 2, j= 1, ii= 3, jj= 2 Legendre integration=-1.04969387755102E+00, at i= 2, j= 1, ii= 3, jj= 3 Legendre integration= 1.61259566326529E-01, at i= 2, j= 1, ii= 3, jj= 4 Legendre integration= 3.59334183673469E+00, at i= 2, j= 2, ii= 2, jj= 1 Legendre integration=-1.57702040816326E+01, at i= 2, j= 2, ii= 2, jj= 2 Legendre integration= 1.09535969387755E+01, at i= 2, j= 2, ii= 2, jj= 3 Legendre integration=-1.95887755102040E+00, at i= 2, j= 2, ii= 2, jj= 4 Legendre integration=-8.01734693877549E-01, at i= 2, j= 2, ii= 3, jj= 1 Legendre integration= 7.04823979591835E+00, at i= 2, j= 2, ii= 3, jj= 2 Legendre integration=-1.57702040816326E+01, at i= 2, j= 2, ii= 3, jj= 3 Legendre integration= 6.34155612244896E+00, at i= 2, j= 2, ii= 3, jj= 4 Legendre integration=-1.29532844387755E+00, at i= 2, j= 3, ii= 2, jj= 1 Legendre integration= 5.87663265306121E+00, at i= 2, j= 3, ii= 2, jj= 2 Legendre integration= 1.92943239795921E-01, at i= 2, j= 3, ii= 2, jj= 3 Legendre integration=-5.79604591836733E-01, at i= 2, j= 3, ii= 2, jj= 4 Legendre integration= 4.90752551020408E-01, at i= 2, j= 3, ii= 3, jj= 1 Legendre integration=-3.41951211734694E+00, at i= 2, j= 3, ii= 3, jj= 2 Legendre integration= 5.87663265306121E+00, at i= 2, j= 3, ii= 3, jj= 3 Legendre integration= 1.24676977040816E+00, at i= 2, j= 3, ii= 3, jj= 4 Legendre integration= 4.22448979591842E-02, at i= 2, j= 4, ii= 2, jj= 1 Legendre integration=-3.38877551020408E-01, at i= 2, j= 4, ii= 2, jj= 2 Legendre integration=-1.06415816326530E+00, at i= 2, j= 4, ii= 2, jj= 3 Legendre integration= 3.56326530612244E-01, at i= 2, j= 4, ii= 2, jj= 4 Legendre integration=-6.79591836734696E-02, at i= 2, j= 4, ii= 3, jj= 1 Legendre integration= 3.67806122448980E-01, at i= 2, j= 4, ii= 3, jj= 2 Legendre integration=-3.38877551020410E-01, at i= 2, j= 4, ii= 3, jj= 3 Legendre integration=-9.65433673469384E-01, at i= 2, j= 4, ii= 3, jj= 4 Legendre integration=-6.71326530612243E-01, at i= 3, j= 1, ii= 2, jj= 1 Legendre integration= 5.86836734693874E-01, at i= 3, j= 1, ii= 2, jj= 2 Legendre integration= 3.51275510204099E-02, at i= 3, j= 1, ii= 2, jj= 3 Legendre integration=-5.51020408163268E-02, at i= 3, j= 1, ii= 2, jj= 4 Legendre integration= 2.40612244897958E-01, at i= 3, j= 1, ii= 3, jj= 1 Legendre integration=-9.62908163265303E-01, at i= 3, j= 1, ii= 3, jj= 2 Legendre integration= 5.86836734693876E-01, at i= 3, j= 1, ii= 3, jj= 3 Legendre integration= 3.09948979591845E-02, at i= 3, j= 1, ii= 3, jj= 4 Legendre integration= 1.11297512755102E+00, at i= 3, j= 2, ii= 2, jj= 1 Legendre integration= 2.75234693877551E+00, at i= 3, j= 2, ii= 2, jj= 2 Legendre integration=-3.51714604591836E+00, at i= 3, j= 2, ii= 2, jj= 3 Legendre integration= 8.08966836734692E-01, at i= 3, j= 2, ii= 2, jj= 4 Legendre integration=-5.50676020408163E-01, at i= 3, j= 2, ii= 3, jj= 1 Legendre integration= 1.07164859693878E+00, at i= 3, j= 2, ii= 3, jj= 2 Legendre integration= 2.75234693877550E+00, at i= 3, j= 2, ii= 3, jj= 3 Legendre integration=-2.11617665816326E+00, at i= 3, j= 2, ii= 3, jj= 4 Legendre integration= 3.59334183673469E+00, at i= 3, j= 3, ii= 2, jj= 1 Legendre integration=-1.57702040816326E+01, at i= 3, j= 3, ii= 2, jj= 2 Legendre integration= 1.09535969387755E+01, at i= 3, j= 3, ii= 2, jj= 3 Legendre integration=-1.95887755102041E+00, at i= 3, j= 3, ii= 2, jj= 4 Legendre integration=-8.01734693877547E-01, at i= 3, j= 3, ii= 3, jj= 1 Legendre integration= 7.04823979591835E+00, at i= 3, j= 3, ii= 3, jj= 2 Legendre integration=-1.57702040816326E+01, at i= 3, j= 3, ii= 3, jj= 3 Legendre integration= 6.34155612244897E+00, at i= 3, j= 3, ii= 3, jj= 4 Legendre integration= 7.72863520408152E-02, at i= 3, j= 4, ii= 2, jj= 1 Legendre integration= 1.14887755102041E+00, at i= 3, j= 4, ii= 2, jj= 2 Legendre integration= 2.67150191326530E+00, at i= 3, j= 4, ii= 2, jj= 3 Legendre integration=-9.24451530612241E-01, at i= 3, j= 4, ii= 2, jj= 4 Legendre integration= 1.07334183673470E-01, at i= 3, j= 4, ii= 3, jj= 1 Legendre integration=-8.10774872448980E-01, at i= 3, j= 4, ii= 3, jj= 2 Legendre integration= 1.14887755102041E+00, at i= 3, j= 4, ii= 3, jj= 3 Legendre integration= 2.52777742346938E+00, at i= 3, j= 4, ii= 3, jj= 4 Legendre integration= 1.99044642857143E+00, i= 2, ii= 2 Legendre integration= 5.64749999999999E+00, i= 2, ii= 3 Legendre integration= 4.46625000000000E+00, i= 3, ii= 2 Legendre integration= 8.42705357142856E+00, i= 3, ii= 3 k computed stiffness matrix, see above f computed forcing function, see above ug computed Galerkin, Ua analytic, error ug( 1, 1)= 1.00000, Ua= 1.00000, err= -0.00000 ug( 1, 2)= 1.03704, Ua= 1.03704, err= -0.00000 ug( 1, 3)= 1.29630, Ua= 1.29630, err= 0.00000 ug( 1, 4)= 2.00000, Ua= 2.00000, err= 0.00000 ug( 2, 1)= 1.03704, Ua= 1.03704, err= 0.00000 ug( 2, 2)= 1.18519, Ua= 1.18519, err= -0.00000 ug( 2, 3)= 1.55556, Ua= 1.55556, err= -0.00000 ug( 2, 4)= 2.37037, Ua= 2.37037, err= 0.00000 ug( 3, 1)= 1.29630, Ua= 1.29630, err= 0.00000 ug( 3, 2)= 1.55556, Ua= 1.55556, err= -0.00000 ug( 3, 3)= 2.03704, Ua= 2.03704, err= -0.00000 ug( 3, 4)= 2.96296, Ua= 2.96296, err= 0.00000 ug( 4, 1)= 2.00000, Ua= 2.00000, err= 0.00000 ug( 4, 2)= 2.37037, Ua= 2.37037, err= 0.00000 ug( 4, 3)= 2.96296, Ua= 2.96296, err= 0.00000 ug( 4, 4)= 4.00000, Ua= 4.00000, err= 0.00000 maxerr= 4.44089209850063E-15, avgerr= 9.15933995315754E-16 end fem_check22_la.adb