20 October 2006 10:42:02 AM FREE_FEM_STOKES (C++ version): Finite element solution of the steady incompressible Stokes equations on a triangulated region in 2 dimensions.' - nu * ( Uxx + Uyy ) + dPdx = F1(x,y) - nu * ( Vxx + Vyy ) + dPdy = F2(x,y) Ux + Vy = F3(x,y). Boundary conditions may be of Dirichlet type: U(x,y) = U_BC(x,y) V(x,y) = V_BC(x,y) P(x,y) = P_BC(x,y) or of Neumann type with zero right hand side: dU/dn(x,y) = 0 dV/dn(x,y) = 0 dP/dn(x,y) = 0 The finite element method uses Taylor-Hood triangular elements which are linear for pressure and quadratic for velocity. The kinematic viscosity NU = 1 Current status: * testing zero Neumann condition option. Node file is "nodes6.txt". Element file is "triangles6.txt". Number of nodes = 289 First 10 nodes Row: 1 2 Col 1 0 0 2 0 0.0625 3 0 0.125 4 0 0.1875 5 0 0.25 6 0 0.3125 7 0 0.375 8 0 0.4375 9 0 0.5 10 0 0.5625 Element order = 6 Number of elements = 128 First 10 elements Row: 1 2 3 4 5 6 Col 1 1 3 37 2 20 19 2 1 37 35 19 36 18 3 3 5 39 4 22 21 4 3 39 37 21 38 20 5 5 7 41 6 24 23 6 5 41 39 23 40 22 7 7 9 43 8 26 25 8 7 43 41 25 42 24 9 9 11 45 10 28 27 10 9 45 43 27 44 26 Quadrature order = 3 Dirichlet boundary condition on pressure will be applied at node 1 Number of Neumann conditions added = 0 Boundary conditions per node: Node U_cond V_cond P_cond 0 2 2 2 1 2 2 0 2 2 2 1 3 2 2 0 4 2 2 1 5 2 2 0 6 2 2 1 7 2 2 0 8 2 2 1 9 2 2 0 10 2 2 1 11 2 2 0 12 2 2 1 13 2 2 0 14 2 2 1 15 2 2 0 16 2 2 1 17 2 2 0 18 1 1 0 19 1 1 0 20 1 1 0 21 1 1 0 22 1 1 0 23 1 1 0 24 1 1 0 25 1 1 0 26 1 1 0 27 1 1 0 28 1 1 0 29 1 1 0 30 1 1 0 31 1 1 0 32 1 1 0 33 2 2 0 34 2 2 1 35 1 1 0 36 1 1 1 37 1 1 0 38 1 1 1 39 1 1 0 40 1 1 1 41 1 1 0 42 1 1 1 43 1 1 0 44 1 1 1 45 1 1 0 46 1 1 1 47 1 1 0 48 1 1 1 49 1 1 0 50 2 2 1 51 2 2 0 52 1 1 0 53 1 1 0 54 1 1 0 55 1 1 0 56 1 1 0 57 1 1 0 58 1 1 0 59 1 1 0 60 1 1 0 61 1 1 0 62 1 1 0 63 1 1 0 64 1 1 0 65 1 1 0 66 1 1 0 67 2 2 0 68 2 2 1 69 1 1 0 70 1 1 1 71 1 1 0 72 1 1 1 73 1 1 0 74 1 1 1 75 1 1 0 76 1 1 1 77 1 1 0 78 1 1 1 79 1 1 0 80 1 1 1 81 1 1 0 82 1 1 1 83 1 1 0 84 2 2 1 85 2 2 0 86 1 1 0 87 1 1 0 88 1 1 0 89 1 1 0 90 1 1 0 91 1 1 0 92 1 1 0 93 1 1 0 94 1 1 0 95 1 1 0 96 1 1 0 97 1 1 0 98 1 1 0 99 1 1 0 100 1 1 0 101 2 2 0 102 2 2 1 103 1 1 0 104 1 1 1 105 1 1 0 106 1 1 1 107 1 1 0 108 1 1 1 109 1 1 0 110 1 1 1 111 1 1 0 112 1 1 1 113 1 1 0 114 1 1 1 115 1 1 0 116 1 1 1 117 1 1 0 118 2 2 1 119 2 2 0 120 1 1 0 121 1 1 0 122 1 1 0 123 1 1 0 124 1 1 0 125 1 1 0 126 1 1 0 127 1 1 0 128 1 1 0 129 1 1 0 130 1 1 0 131 1 1 0 132 1 1 0 133 1 1 0 134 1 1 0 135 2 2 0 136 2 2 1 137 1 1 0 138 1 1 1 139 1 1 0 140 1 1 1 141 1 1 0 142 1 1 1 143 1 1 0 144 1 1 1 145 1 1 0 146 1 1 1 147 1 1 0 148 1 1 1 149 1 1 0 150 1 1 1 151 1 1 0 152 2 2 1 153 2 2 0 154 1 1 0 155 1 1 0 156 1 1 0 157 1 1 0 158 1 1 0 159 1 1 0 160 1 1 0 161 1 1 0 162 1 1 0 163 1 1 0 164 1 1 0 165 1 1 0 166 1 1 0 167 1 1 0 168 1 1 0 169 2 2 0 170 2 2 1 171 1 1 0 172 1 1 1 173 1 1 0 174 1 1 1 175 1 1 0 176 1 1 1 177 1 1 0 178 1 1 1 179 1 1 0 180 1 1 1 181 1 1 0 182 1 1 1 183 1 1 0 184 1 1 1 185 1 1 0 186 2 2 1 187 2 2 0 188 1 1 0 189 1 1 0 190 1 1 0 191 1 1 0 192 1 1 0 193 1 1 0 194 1 1 0 195 1 1 0 196 1 1 0 197 1 1 0 198 1 1 0 199 1 1 0 200 1 1 0 201 1 1 0 202 1 1 0 203 2 2 0 204 2 2 1 205 1 1 0 206 1 1 1 207 1 1 0 208 1 1 1 209 1 1 0 210 1 1 1 211 1 1 0 212 1 1 1 213 1 1 0 214 1 1 1 215 1 1 0 216 1 1 1 217 1 1 0 218 1 1 1 219 1 1 0 220 2 2 1 221 2 2 0 222 1 1 0 223 1 1 0 224 1 1 0 225 1 1 0 226 1 1 0 227 1 1 0 228 1 1 0 229 1 1 0 230 1 1 0 231 1 1 0 232 1 1 0 233 1 1 0 234 1 1 0 235 1 1 0 236 1 1 0 237 2 2 0 238 2 2 1 239 1 1 0 240 1 1 1 241 1 1 0 242 1 1 1 243 1 1 0 244 1 1 1 245 1 1 0 246 1 1 1 247 1 1 0 248 1 1 1 249 1 1 0 250 1 1 1 251 1 1 0 252 1 1 1 253 1 1 0 254 2 2 1 255 2 2 0 256 1 1 0 257 1 1 0 258 1 1 0 259 1 1 0 260 1 1 0 261 1 1 0 262 1 1 0 263 1 1 0 264 1 1 0 265 1 1 0 266 1 1 0 267 1 1 0 268 1 1 0 269 1 1 0 270 1 1 0 271 2 2 0 272 2 2 1 273 2 2 0 274 2 2 1 275 2 2 0 276 2 2 1 277 2 2 0 278 2 2 1 279 2 2 0 280 2 2 1 281 2 2 0 282 2 2 1 283 2 2 0 284 2 2 1 285 2 2 0 286 2 2 1 287 2 2 0 288 2 2 1 Total number of variables is 659 Variable indices per node: Node U_index V_index P_index 1 1 2 3 2 4 5 -1 3 6 7 8 4 9 10 -1 5 11 12 13 6 14 15 -1 7 16 17 18 8 19 20 -1 9 21 22 23 10 24 25 -1 11 26 27 28 12 29 30 -1 13 31 32 33 14 34 35 -1 15 36 37 38 16 39 40 -1 17 41 42 43 18 44 45 -1 19 46 47 -1 20 48 49 -1 21 50 51 -1 22 52 53 -1 23 54 55 -1 24 56 57 -1 25 58 59 -1 26 60 61 -1 27 62 63 -1 28 64 65 -1 29 66 67 -1 30 68 69 -1 31 70 71 -1 32 72 73 -1 33 74 75 -1 34 76 77 -1 35 78 79 80 36 81 82 -1 37 83 84 85 38 86 87 -1 39 88 89 90 40 91 92 -1 41 93 94 95 42 96 97 -1 43 98 99 100 44 101 102 -1 45 103 104 105 46 106 107 -1 47 108 109 110 48 111 112 -1 49 113 114 115 50 116 117 -1 51 118 119 120 52 121 122 -1 53 123 124 -1 54 125 126 -1 55 127 128 -1 56 129 130 -1 57 131 132 -1 58 133 134 -1 59 135 136 -1 60 137 138 -1 61 139 140 -1 62 141 142 -1 63 143 144 -1 64 145 146 -1 65 147 148 -1 66 149 150 -1 67 151 152 -1 68 153 154 -1 69 155 156 157 70 158 159 -1 71 160 161 162 72 163 164 -1 73 165 166 167 74 168 169 -1 75 170 171 172 76 173 174 -1 77 175 176 177 78 178 179 -1 79 180 181 182 80 183 184 -1 81 185 186 187 82 188 189 -1 83 190 191 192 84 193 194 -1 85 195 196 197 86 198 199 -1 87 200 201 -1 88 202 203 -1 89 204 205 -1 90 206 207 -1 91 208 209 -1 92 210 211 -1 93 212 213 -1 94 214 215 -1 95 216 217 -1 96 218 219 -1 97 220 221 -1 98 222 223 -1 99 224 225 -1 100 226 227 -1 101 228 229 -1 102 230 231 -1 103 232 233 234 104 235 236 -1 105 237 238 239 106 240 241 -1 107 242 243 244 108 245 246 -1 109 247 248 249 110 250 251 -1 111 252 253 254 112 255 256 -1 113 257 258 259 114 260 261 -1 115 262 263 264 116 265 266 -1 117 267 268 269 118 270 271 -1 119 272 273 274 120 275 276 -1 121 277 278 -1 122 279 280 -1 123 281 282 -1 124 283 284 -1 125 285 286 -1 126 287 288 -1 127 289 290 -1 128 291 292 -1 129 293 294 -1 130 295 296 -1 131 297 298 -1 132 299 300 -1 133 301 302 -1 134 303 304 -1 135 305 306 -1 136 307 308 -1 137 309 310 311 138 312 313 -1 139 314 315 316 140 317 318 -1 141 319 320 321 142 322 323 -1 143 324 325 326 144 327 328 -1 145 329 330 331 146 332 333 -1 147 334 335 336 148 337 338 -1 149 339 340 341 150 342 343 -1 151 344 345 346 152 347 348 -1 153 349 350 351 154 352 353 -1 155 354 355 -1 156 356 357 -1 157 358 359 -1 158 360 361 -1 159 362 363 -1 160 364 365 -1 161 366 367 -1 162 368 369 -1 163 370 371 -1 164 372 373 -1 165 374 375 -1 166 376 377 -1 167 378 379 -1 168 380 381 -1 169 382 383 -1 170 384 385 -1 171 386 387 388 172 389 390 -1 173 391 392 393 174 394 395 -1 175 396 397 398 176 399 400 -1 177 401 402 403 178 404 405 -1 179 406 407 408 180 409 410 -1 181 411 412 413 182 414 415 -1 183 416 417 418 184 419 420 -1 185 421 422 423 186 424 425 -1 187 426 427 428 188 429 430 -1 189 431 432 -1 190 433 434 -1 191 435 436 -1 192 437 438 -1 193 439 440 -1 194 441 442 -1 195 443 444 -1 196 445 446 -1 197 447 448 -1 198 449 450 -1 199 451 452 -1 200 453 454 -1 201 455 456 -1 202 457 458 -1 203 459 460 -1 204 461 462 -1 205 463 464 465 206 466 467 -1 207 468 469 470 208 471 472 -1 209 473 474 475 210 476 477 -1 211 478 479 480 212 481 482 -1 213 483 484 485 214 486 487 -1 215 488 489 490 216 491 492 -1 217 493 494 495 218 496 497 -1 219 498 499 500 220 501 502 -1 221 503 504 505 222 506 507 -1 223 508 509 -1 224 510 511 -1 225 512 513 -1 226 514 515 -1 227 516 517 -1 228 518 519 -1 229 520 521 -1 230 522 523 -1 231 524 525 -1 232 526 527 -1 233 528 529 -1 234 530 531 -1 235 532 533 -1 236 534 535 -1 237 536 537 -1 238 538 539 -1 239 540 541 542 240 543 544 -1 241 545 546 547 242 548 549 -1 243 550 551 552 244 553 554 -1 245 555 556 557 246 558 559 -1 247 560 561 562 248 563 564 -1 249 565 566 567 250 568 569 -1 251 570 571 572 252 573 574 -1 253 575 576 577 254 578 579 -1 255 580 581 582 256 583 584 -1 257 585 586 -1 258 587 588 -1 259 589 590 -1 260 591 592 -1 261 593 594 -1 262 595 596 -1 263 597 598 -1 264 599 600 -1 265 601 602 -1 266 603 604 -1 267 605 606 -1 268 607 608 -1 269 609 610 -1 270 611 612 -1 271 613 614 -1 272 615 616 -1 273 617 618 619 274 620 621 -1 275 622 623 624 276 625 626 -1 277 627 628 629 278 630 631 -1 279 632 633 634 280 635 636 -1 281 637 638 639 282 640 641 -1 283 642 643 644 284 645 646 -1 285 647 648 649 286 650 651 -1 287 652 653 654 288 655 656 -1 289 657 658 659 The matrix half bandwidth is 84 The matrix bandwidth is 169 The storage bandwidth is 253 Solution values associated with nodes: Node U V P 0 0 0 0 1 0.75 -2.73219e-17 2 1 2.84928e-16 -0.205428 3 0.75 8.32667e-17 4 3.33067e-16 8.32667e-17 -31.7871 5 -1.66533e-16 0 6 3.33067e-16 -1.66533e-16 -26.8265 7 -3.33067e-16 1.66533e-16 8 -1.66533e-16 1.66533e-16 -26.3111 9 -3.33067e-16 -1.66533e-16 10 -1.66533e-16 -8.32667e-17 -26.322 11 8.32667e-17 1.66533e-16 12 1.66533e-16 2.498e-16 -26.0903 13 -4.16334e-16 -8.32667e-17 14 -1.66533e-16 -2.498e-16 -25.8051 15 8.32667e-17 -8.32667e-17 16 0 0 -25.701 17 0 0 18 0.685006 0.0733953 19 0.900053 0.203188 20 0.652512 0.389715 21 0.195913 0.374095 22 0.0474322 0.177964 23 0.0153156 0.103151 24 0.00820498 0.0865366 25 0.0103157 0.0635672 26 0.00854567 0.0482425 27 0.00630345 0.0349284 28 0.00510234 0.0231404 29 0.00419808 0.0137188 30 0.00307681 0.00652703 31 0.0016838 0.00184239 32 3.82502e-05 3.82502e-05 33 0 0 34 0 8.32667e-17 -18.0511 35 0.53841 0.0965067 36 0.723662 0.253067 -17.4544 37 0.62515 0.394746 38 0.344872 0.414004 -23.4299 39 0.140925 0.290888 40 0.0693089 0.207539 -24.7886 41 0.0447428 0.169404 42 0.0359374 0.127935 -25.9455 43 0.0295509 0.0946964 44 0.0241154 0.0693797 -25.9204 45 0.0200567 0.0487535 46 0.0163613 0.031025 -25.8424 47 0.0119145 0.0172001 48 0.00685039 0.00703626 -25.7018 49 0.00184851 0.00171337 50 0 0 -25.5881 51 -1.35654e-16 -3.76662e-16 52 0.386772 0.0782123 53 0.548776 0.20672 54 0.511635 0.335464 55 0.36103 0.37486 56 0.230168 0.321581 57 0.151676 0.264853 58 0.104106 0.219454 59 0.0752826 0.175814 60 0.0596796 0.134013 61 0.0500493 0.101447 62 0.0429691 0.0739071 63 0.0360547 0.0490682 64 0.0273869 0.0286066 65 0.0172712 0.0127687 66 0.00682792 0.0033308 67 0 0 68 0 -3.33067e-16 -24.3518 69 0.285304 0.0505691 70 0.420735 0.153837 -22.328 71 0.437027 0.256541 72 0.360636 0.309699 -23.3278 73 0.266133 0.309168 74 0.198122 0.280775 -24.9487 75 0.148964 0.240835 76 0.114895 0.20179 -25.5139 77 0.0949418 0.162496 78 0.0821575 0.127784 -25.6412 79 0.0721244 0.0964823 80 0.0615947 0.0662471 -25.7114 81 0.0484971 0.0398804 82 0.0323062 0.0186384 -25.5646 83 0.0150427 0.00495708 84 0 0 -25.2868 85 1.54938e-16 -1.27204e-16 86 0.202392 0.0334722 87 0.324171 0.10852 88 0.359828 0.19592 89 0.331741 0.251303 90 0.275884 0.273964 91 0.220913 0.268364 92 0.178568 0.243658 93 0.148169 0.215333 94 0.12941 0.182418 95 0.116982 0.148972 96 0.105728 0.115798 97 0.0925597 0.0820043 98 0.0751122 0.0506172 99 0.0525405 0.0241976 100 0.0261866 0.0065392 101 0 0 102 0 0 -25.5604 103 0.148341 0.0240609 104 0.247994 0.0805956 -24.4315 105 0.294383 0.149814 106 0.292368 0.202489 -24.5517 107 0.264309 0.234177 108 0.228446 0.244554 -25.0329 109 0.197244 0.236087 110 0.174471 0.219942 -25.3645 111 0.159514 0.196188 112 0.149897 0.16676 -25.6648 113 0.140466 0.133498 114 0.126983 0.0973279 -25.7377 115 0.106806 0.06175 116 0.0772868 0.0302714 -25.5413 117 0.0405351 0.00832397 118 0 0 -25.0944 119 -1.53564e-16 2.51749e-16 120 0.110334 0.0174536 121 0.191598 0.0602723 122 0.235607 0.116494 123 0.24717 0.16488 124 0.23805 0.200664 125 0.22007 0.220887 126 0.203223 0.225832 127 0.19091 0.220721 128 0.183586 0.206249 129 0.179589 0.182939 130 0.174986 0.151828 131 0.16454 0.114546 132 0.143473 0.0749225 133 0.108035 0.0373336 134 0.0585279 0.0104489 135 0 0 136 0 1.66533e-16 -25.9801 137 0.0810788 0.0135567 138 0.144937 0.0471977 -25.3121 139 0.186648 0.0921423 140 0.204916 0.13598 -25.1193 141 0.20842 0.173178 142 0.203835 0.200213 -25.2482 143 0.198354 0.215685 144 0.196459 0.220912 -25.5534 145 0.198354 0.215685 146 0.203835 0.200213 -25.8585 147 0.20842 0.173178 148 0.204916 0.13598 -25.9874 149 0.186648 0.0921423 150 0.144937 0.0471977 -25.7946 151 0.0810788 0.0135567 152 0 0 -25.1267 153 -1.11719e-15 8.595e-17 154 0.0585279 0.0104489 155 0.108035 0.0373336 156 0.143473 0.0749225 157 0.16454 0.114546 158 0.174986 0.151828 159 0.179589 0.182939 160 0.183586 0.206249 161 0.19091 0.220721 162 0.203223 0.225832 163 0.22007 0.220887 164 0.23805 0.200664 165 0.24717 0.16488 166 0.235607 0.116494 167 0.191598 0.0602723 168 0.110334 0.0174536 169 0 0 170 0 1.66533e-16 -26.0123 171 0.0405351 0.00832397 172 0.0772868 0.0302714 -25.5655 173 0.106806 0.06175 174 0.126983 0.0973279 -25.369 175 0.140466 0.133498 176 0.149897 0.16676 -25.4419 177 0.159514 0.196188 178 0.174471 0.219942 -25.7422 179 0.197244 0.236087 180 0.228446 0.244554 -26.0738 181 0.264309 0.234177 182 0.292368 0.202489 -26.555 183 0.294383 0.149814 184 0.247994 0.0805956 -26.6752 185 0.148341 0.0240609 186 0 0 -25.5463 187 6.23935e-19 -3.49243e-17 188 0.0261866 0.0065392 189 0.0525405 0.0241976 190 0.0751122 0.0506172 191 0.0925597 0.0820043 192 0.105728 0.115798 193 0.116982 0.148972 194 0.12941 0.182418 195 0.148169 0.215333 196 0.178568 0.243658 197 0.220913 0.268364 198 0.275884 0.273964 199 0.331741 0.251303 200 0.359828 0.19592 201 0.324171 0.10852 202 0.202392 0.0334722 203 0 0 204 0 -1.66533e-16 -25.8199 205 0.0150427 0.00495708 206 0.0323062 0.0186384 -25.5421 207 0.0484971 0.0398804 208 0.0615947 0.0662471 -25.3953 209 0.0721244 0.0964823 210 0.0821575 0.127784 -25.4655 211 0.0949418 0.162496 212 0.114895 0.20179 -25.5928 213 0.148964 0.240835 214 0.198122 0.280775 -26.158 215 0.266133 0.309168 216 0.360636 0.309699 -27.7789 217 0.437027 0.256541 218 0.420735 0.153837 -28.7787 219 0.285304 0.0505691 220 0 0 -26.7549 221 -1.20585e-16 2.78718e-17 222 0.00682792 0.0033308 223 0.0172712 0.0127687 224 0.0273869 0.0286066 225 0.0360547 0.0490682 226 0.0429691 0.0739071 227 0.0500493 0.101447 228 0.0596796 0.134013 229 0.0752826 0.175814 230 0.104106 0.219454 231 0.151676 0.264853 232 0.230168 0.321581 233 0.36103 0.37486 234 0.511635 0.335464 235 0.548776 0.20672 236 0.386772 0.0782123 237 0 0 238 0 -1.66533e-16 -25.5186 239 0.00184851 0.00171337 240 0.00685039 0.00703626 -25.4049 241 0.0119145 0.0172001 242 0.0163613 0.031025 -25.2643 243 0.0200567 0.0487535 244 0.0241154 0.0693797 -25.1863 245 0.0295509 0.0946964 246 0.0359374 0.127935 -25.1612 247 0.0447428 0.169404 248 0.0693089 0.207539 -26.3181 249 0.140925 0.290888 250 0.344872 0.414004 -27.6769 251 0.62515 0.394746 252 0.723662 0.253067 -33.6523 253 0.53841 0.0965067 254 0 0 -33.0556 255 0 0 256 3.82502e-05 3.82502e-05 257 0.0016838 0.00184239 258 0.00307681 0.00652703 259 0.00419808 0.0137188 260 0.00510234 0.0231404 261 0.00630345 0.0349284 262 0.00854567 0.0482425 263 0.0103157 0.0635672 264 0.00820498 0.0865366 265 0.0153156 0.103151 266 0.0474322 0.177964 267 0.195913 0.374095 268 0.652512 0.389715 269 0.900053 0.203188 270 0.685006 0.0733953 271 0 0 272 0 0 -25.4057 273 0 0 274 0 0 -25.3016 275 0 0 276 0 0 -25.0164 277 0 0 278 0 0 -24.7847 279 0 0 280 0 0 -24.7956 281 0 0 282 0 0 -24.2802 283 0 0 284 0 0 -19.3196 285 0.75 0 286 1 0 -50.9013 287 0.75 0 288 0 0 -51.1067 Pressure nodes written to "nodes3.txt". Pressure triangles written to "triangles3.txt". Pressures written to "pressure3.txt". Velocities written to "velocity6.txt". FREE_FEM_STOKES: Normal end of execution. 20 October 2006 10:42:03 AM