forward_euler: FreeFem++ version. Solve a time-dependent boundary value problem in a square. Use the Forward Euler method to handle the time variation. At each time, report the L2 norm, L2 error norm, and L2 relative error norm. At the end, report infinity(T) L2(X) and L2(T) L2(X) error norms. H = 0.0625 DT = 0.0002 T ||Exact|| ||Error|| ||Error||/||Exact|| 0 0.5 0.00392323 0.00784645 0.0002 0.4999 0.00393049 0.00786256 0.0004 0.4998 0.00393761 0.00787838 0.0006 0.4997 0.00394461 0.00789395 0.0008 0.4996 0.0039515 0.00790932 0.001 0.4995 0.00395829 0.00792449 0.0012 0.4994 0.00396499 0.0079395 0.0014 0.4993 0.0039716 0.00795434 0.0016 0.499201 0.00397814 0.00796903 0.0018 0.499101 0.00398461 0.00798357 0.002 0.499001 0.003991 0.00799799 0.0022 0.498901 0.00399733 0.00801227 0.0024 0.498801 0.00400359 0.00802642 0.0026 0.498702 0.00400979 0.00804046 0.0028 0.498602 0.00401593 0.00805438 0.003 0.498502 0.00402201 0.00806819 0.0032 0.498403 0.00402804 0.00808189 0.0034 0.498303 0.00403401 0.00809549 0.0036 0.498203 0.00403992 0.00810898 0.0038 0.498104 0.00404578 0.00812237 0.004 0.498004 0.0040516 0.00813567 0.0042 0.497904 0.00405736 0.00814887 0.0044 0.497805 0.00406307 0.00816198 0.0046 0.497705 0.00406874 0.00817499 0.0048 0.497606 0.00407436 0.00818792 0.005 0.497506 0.00407993 0.00820076 0.0052 0.497407 0.00408546 0.00821351 0.0054 0.497307 0.00409094 0.00822618 0.0056 0.497208 0.00409638 0.00823877 0.0058 0.497108 0.00410178 0.00825128 0.006 0.497009 0.00410714 0.00826371 0.0062 0.49691 0.00411245 0.00827605 0.0064 0.49681 0.00411773 0.00828833 0.0066 0.496711 0.00412296 0.00830052 0.0068 0.496612 0.00412816 0.00831265 0.007 0.496512 0.00413331 0.00832469 0.0072 0.496413 0.00413843 0.00833667 0.0074 0.496314 0.00414351 0.00834857 0.0076 0.496214 0.00414856 0.00836041 0.0078 0.496115 0.00415356 0.00837217 0.008 0.496016 0.00415853 0.00838387 0.0082 0.495917 0.00416347 0.0083955 0.0084 0.495818 0.00416837 0.00840706 0.0086 0.495718 0.00417324 0.00841856 0.0088 0.495619 0.00417807 0.00842999 0.009 0.49552 0.00418286 0.00844136 0.0092 0.495421 0.00418763 0.00845267 0.0094 0.495322 0.00419236 0.00846391 0.0096 0.495223 0.00419706 0.00847509 0.0098 0.495124 0.00420172 0.00848621 0.01 0.495025 0.00420636 0.00849727 0.0102 0.494926 0.00421096 0.00850827 0.0104 0.494827 0.00421553 0.00851921 0.0106 0.494728 0.00422007 0.00853009 0.0108 0.494629 0.00422459 0.00854092 0.011 0.49453 0.00422907 0.00855168 0.0112 0.494431 0.00423352 0.00856239 0.0114 0.494332 0.00423794 0.00857305 0.0116 0.494234 0.00424233 0.00858365 0.0118 0.494135 0.00424669 0.0085942 0.012 0.494036 0.00425102 0.00860469 0.0122 0.493937 0.00425533 0.00861512 0.0124 0.493838 0.00425961 0.00862551 0.0126 0.49374 0.00426386 0.00863584 0.0128 0.493641 0.00426808 0.00864612 0.013 0.493542 0.00427227 0.00865635 0.0132 0.493443 0.00427644 0.00866653 0.0134 0.493345 0.00428058 0.00867665 0.0136 0.493246 0.00428469 0.00868673 0.0138 0.493147 0.00428878 0.00869676 0.014 0.493049 0.00429284 0.00870673 0.0142 0.49295 0.00429688 0.00871666 0.0144 0.492852 0.00430089 0.00872654 0.0146 0.492753 0.00430487 0.00873637 0.0148 0.492654 0.00430883 0.00874616 0.015 0.492556 0.00431277 0.0087559 0.0152 0.492457 0.00431668 0.00876559 0.0154 0.492359 0.00432056 0.00877523 0.0156 0.492261 0.00432443 0.00878483 0.0158 0.492162 0.00432826 0.00879439 0.016 0.492064 0.00433208 0.00880389 0.0162 0.491965 0.00433587 0.00881336 0.0164 0.491867 0.00433963 0.00882278 0.0166 0.491769 0.00434337 0.00883215 0.0168 0.49167 0.00434709 0.00884148 0.017 0.491572 0.00435079 0.00885077 0.0172 0.491474 0.00435446 0.00886002 0.0174 0.491375 0.00435811 0.00886922 0.0176 0.491277 0.00436174 0.00887838 0.0178 0.491179 0.00436535 0.0088875 0.018 0.491081 0.00436893 0.00889657 0.0182 0.490982 0.0043725 0.00890561 0.0184 0.490884 0.00437604 0.0089146 0.0186 0.490786 0.00437955 0.00892355 0.0188 0.490688 0.00438305 0.00893247 0.019 0.49059 0.00438653 0.00894134 0.0192 0.490492 0.00438998 0.00895017 0.0194 0.490393 0.00439342 0.00895896 0.0196 0.490295 0.00439683 0.00896772 0.0198 0.490197 0.00440022 0.00897643 0.02 0.490099 0.0044036 0.00898511 ||error||_oo,0 = 8.80719e-05 ||error||_0,0 = 8.3897e-06 forward_euler: Normal end of execution. current line = 218 exit(0) err code 0 , mpirank 0