Finite Element Method of BBM-Burgers Equation with Dissipative Term Based on Adaptive Moving Mesh

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/ddns/volume-2017/3427376/figures/3427376.fig.007a.svgz" name="3427376.fig.007a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Moving mesh</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/ddns/volume-2017/3427376/figures/3427376.fig.007b.svgz" name="3427376.fig.007b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>The corresponding numerical solution</td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/ddns/volume-2017/3427376/figures/3427376.fig.007c.svgz" name="3427376.fig.007c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>Fixed mesh</td></tr><tr class="fig-image" id="d"><td><object data="https://static.hindawi.com/articles/ddns/volume-2017/3427376/figures/3427376.fig.007d.svgz" name="3427376.fig.007d" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(d) </b>The corresponding numerical solution</td></tr></table>

<div>Example <a href="https://static.hindawi.com/articles/ddns/volume-2017/3427376/figures/#ex4">4</a>. Meshes (a, c) and the corresponding numerical solutions (b, d) with <span class="nowrap"><svg height="8.8423pt" id="M348" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 51.0244 8.8423" width="51.0244pt" 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="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z" id="g113-79"></path></g><g transform="matrix(.013,0,0,-0.013,14.542,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,25.805,0)"><path d="M137 343C167 482 260 545 321 574C357 591 397 603 429 609L423 641C382 634 335 622 295 608C189 570 37 457 37 238C37 84 125 -12 242 -12C362 -12 447 89 447 209C447 311 374 393 267 393C247 393 226 386 204 376L137 343ZM227 337C318 337 361 256 361 173C361 105 336 22 258 22C176 22 126 120 126 240C126 266 127 291 132 310C155 323 189 337 227 337Z" id="g113-55"></path></g><g transform="matrix(.013,0,0,-0.013,32.045,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z" id="g113-53"></path></g><g transform="matrix(.013,0,0,-0.013,38.285,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g><g transform="matrix(.013,0,0,-0.013,44.525,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g></svg>.</span></div>

Discrete Dynamics in Nature and Society

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Figure 7

Figure 7: Finite Element Method of BBM-Burgers Equation with Dissipative Term Based on Adaptive Moving Mesh 