A Framework for Nonconforming Mixed Finite Element Method for Elliptic Problems in <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.06569958pt" id="M1" height="15.3664pt" version="1.1" viewBox="-0.0657574 -15.3007 19.5274 15.3664" width="19.5274pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g197-29" d="M712 0L497 285C582 312 628 378 628 466C628 609 518 662 390 662H70V0H236V271H310L505 0H712ZM491 604C551 577 584 532 584 464C584 401 550 345 491 321V604ZM447 320C428 317 411 315 392 315H236V618H397C412 618 432 613 447 610V320ZM626 44H528L363 271C392 271 422 270 451 275L626 44ZM192 44H114V618H192V44Z"/></g><g transform="matrix(.012,0,0,-0.012,12.819,-7.578)"><path id="g50-52" d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"/></g></svg>

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left">Level</td><td class="align_center"><span style="width: 54.1012ptpx;"><svg height="12.7178pt" id="M236" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 54.1012 12.7178" width="54.1012pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M162 -163V703H102V-163H162ZM309 -163V703H249V-163H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,5.343,0)"><path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.959,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.495,0)"><path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,33.879,3.132)"><path d="M509 90L493 118C465 91 427 70 418 70S409 77 415 103L469 327C494 429 466 451 436 451C412 451 387 444 356 427C307 400 222 342 160 264H158L246 667C253 701 252 710 243 710C228 710 169 680 87 673L83 644H117C155 644 160 640 149 588L24 -4L32 -12C57 -4 86 4 108 9L143 187C198 275 324 386 375 386C394 386 399 367 385 311L331 87C315 22 322 -12 351 -12C387 -12 452 24 509 90Z"></path></g><g transform="matrix(.013,0,0,-0.013,39.191,0)"><path d="M162 -163V703H102V-163H162ZM309 -163V703H249V-163H309Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,44.534,3.132)"><path d="M567 167L534 181C505 122 482 94 454 70C428 46 385 42 330 42C288 42 248 44 235 55C216 70 213 91 220 130L295 528C310 609 314 611 401 618L409 650H140L131 618C222 611 224 609 209 528L133 126C118 47 108 41 25 33L18 0H497C514 33 554 126 567 167Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,49.636,-.065)"><path d="M452 139L416 148C386 81 373 77 319 77H141L282 220C372 312 414 373 414 464C414 569 332 635 240 635C181 635 132 609 101 574L42 493L70 467C98 506 143 562 209 562C280 562 324 515 324 435C324 347 261 272 197 197C148 139 89 84 34 29V0H417L452 139Z"></path></g></svg></span></td><td class="align_center">Order</td><td class="align_center"><span style="width: 70.3028ptpx;"><svg height="13.9678pt" id="M237" style="vertical-align:-4.67947pt" version="1.1" viewbox="-0.0498162 -9.28833 70.3028 13.9678" width="70.3028pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M162 -163V703H102V-163H162ZM309 -163V703H249V-163H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,5.343,0)"><path d="M542 56L520 58C483 62 478 72 478 124V449C455 445 422 441 387 438C351 435 316 432 287 431V402L318 395C345 389 350 383 350 336V93C328 71 306 65 279 65C245 65 211 88 211 153V298C211 356 211 407 214 449C187 445 151 441 118 438C84 435 53 432 28 431V402L51 395C77 388 83 383 83 337V130C83 42 131 -12 214 -12C245 -12 272 -1 300 18C322 31 333 41 350 55V-5L359 -12C389 -5 420 2 452 8C485 15 513 20 542 24V56Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.464,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,26,0)"><path d="M542 56L520 58C483 62 478 72 478 124V449C455 445 422 441 387 438C351 435 316 432 287 431V402L318 395C345 389 350 383 350 336V93C328 71 306 65 279 65C245 65 211 88 211 153V298C211 356 211 407 214 449C187 445 151 441 118 438C84 435 53 432 28 431V402L51 395C77 388 83 383 83 337V130C83 42 131 -12 214 -12C245 -12 272 -1 300 18C322 31 333 41 350 55V-5L359 -12C389 -5 420 2 452 8C485 15 513 20 542 24V56Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,33.215,3.132)"><path d="M509 90L493 118C465 91 427 70 418 70S409 77 415 103L469 327C494 429 466 451 436 451C412 451 387 444 356 427C307 400 222 342 160 264H158L246 667C253 701 252 710 243 710C228 710 169 680 87 673L83 644H117C155 644 160 640 149 588L24 -4L32 -12C57 -4 86 4 108 9L143 187C198 275 324 386 375 386C394 386 399 367 385 311L331 87C315 22 322 -12 351 -12C387 -12 452 24 509 90Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.527,0)"><path d="M162 -163V703H102V-163H162ZM309 -163V703H249V-163H309Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,43.87,3.132)"><path d="M870 650H600L593 618C681 609 684 605 669 516L641 367H261L286 516C302 603 313 610 391 618L398 650H132L123 618C214 610 218 606 200 516L127 130C113 46 107 40 25 32L18 0H290L298 32C204 40 200 42 214 130L250 321H631L596 131C580 47 573 39 484 32L475 0H753L762 32C673 39 668 46 685 130L757 516C772 606 778 610 861 618L870 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,51.58,3.132)"><path d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,54.838,3.132)"><path d="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,59.642,3.132)"><path d="M135 536C164 536 186 560 186 587C186 617 164 639 136 639C109 639 85 617 85 587C85 560 109 536 135 536ZM252 0V26C188 32 181 38 181 106V451C138 433 90 420 39 412V388C99 379 102 374 102 312V106C102 38 95 32 32 26V0H252Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,62.017,3.132)"><path d="M478 437H300V411C357 404 363 393 347 345C325 280 293 190 258 107C229 178 188 284 163 354C147 397 149 405 203 411V437H-2V411C52 403 59 396 82 339C130 222 176 109 220 -11H248C304 138 356 261 390 336C417 395 425 404 478 411V437Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,66.273,3.132)"><path d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z"></path></g></svg></span></td><td class="align_center">Order</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">1</td><td class="align_center">1.324<i>E</i> − 05</td><td class="align_left"> </td><td class="align_center">2.608<i>E</i> − 03</td><td class="align_left"> </td></tr><tr><td class="align_left">2</td><td class="align_center">5.113<i>E</i> − 06</td><td class="align_center">1.373</td><td class="align_center">8.617<i>E</i> − 04</td><td class="align_center">1.597</td></tr><tr><td class="align_left">3</td><td class="align_center">1.469<i>E</i> − 06</td><td class="align_center">1.799</td><td class="align_center">2.327<i>E</i> − 04</td><td class="align_center">1.889</td></tr><tr><td class="align_left">4</td><td class="align_center">3.802<i>E</i> − 07</td><td class="align_center">1.950</td><td class="align_center">5.932<i>E</i> − 05</td><td class="align_center">1.972</td></tr><tr><td class="align_left">5</td><td class="align_center">9.587<i>E</i> − 08</td><td class="align_center">1.988</td><td class="align_center">1.490<i>E</i> − 05</td><td class="align_center">1.993</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div><span class="nowrap"><svg height="11.6412pt" id="M234" style="vertical-align:-0.04979992pt" version="1.1" viewbox="-0.0498162 -11.5914 12.262 11.6412" width="12.262pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.185,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g></svg>-</span>error for pressure and <span class="nowrap"><svg height="11.576pt" id="M235" style="vertical-align:-2.2681pt" version="1.1" viewbox="-0.0498162 -9.3079 36.4273 11.576" width="36.4273pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M828 650H570L564 622C646 614 650 609 634 524L604 366H253L281 524C296 608 308 615 382 622L388 650H132L126 622C211 615 214 609 198 524L121 122C106 42 102 35 23 28L17 0H276L282 28C196 35 191 40 206 122L243 324H597L559 123C544 42 537 35 452 28L446 0H710L716 28C632 35 628 43 643 122L719 524C735 610 741 615 822 622L828 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.923,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.421,0)"><path d="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.285,0)"><path d="M135 536C164 536 186 560 186 587C186 617 164 639 136 639C109 639 85 617 85 587C85 560 109 536 135 536ZM252 0V26C188 32 181 38 181 106V451C138 433 90 420 39 412V388C99 379 102 374 102 312V106C102 38 95 32 32 26V0H252Z"></path></g><g transform="matrix(.013,0,0,-0.013,25.678,0)"><path d="M478 437H300V411C357 404 363 393 347 345C325 280 293 190 258 107C229 178 188 284 163 354C147 397 149 405 203 411V437H-2V411C52 403 59 396 82 339C130 222 176 109 220 -11H248C304 138 356 261 390 336C417 395 425 404 478 411V437Z"></path></g><g transform="matrix(.013,0,0,-0.013,31.758,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg>-</span>error of velocity (Example <a href="https://static-preview.hindawi.com/articles/jam/volume-2020/2684630/figures/#ex2" target="_blank">2</a>).</div>

Journal of Applied Mathematics

tab2

Table 2

Table 2: A Framework for Nonconforming Mixed Finite Element Method for Elliptic Problems in <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.06569958pt" id="M1" height="15.3664pt" version="1.1" viewBox="-0.0657574 -15.3007 19.5274 15.3664" width="19.5274pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g197-29" d="M712 0L497 285C582 312 628 378 628 466C628 609 518 662 390 662H70V0H236V271H310L505 0H712ZM491 604C551 577 584 532 584 464C584 401 550 345 491 321V604ZM447 320C428 317 411 315 392 315H236V618H397C412 618 432 613 447 610V320ZM626 44H528L363 271C392 271 422 270 451 275L626 44ZM192 44H114V618H192V44Z"/></g><g transform="matrix(.012,0,0,-0.012,12.819,-7.578)"><path id="g50-52" d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"/></g></svg> 