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Update documentation
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JSchoeberl committed Apr 24, 2024
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8 changes: 4 additions & 4 deletions _sources/aposteriori/aposteriori.ipynb
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"### Red-Green Refinement\n",
"A marked element is split into four equivalent elements (called red refinement):\n",
"\n",
"![](refine_irreg.pdf)\n",
"<img src=\"refine_irreg.png\" alt=\"Alternative text\" width=\"300\" align=\"center\"/>\n",
"\n",
"But, the obtained mesh is not regular. To avoid such irregular nodes,\n",
"also neighboring elements must be split (called green closure):\n",
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"\n",
"If one continues to refine that way, the shape of the elements may get worse and worse:\n",
"\n",
"![](refinebad.pdf)\n",
"<img src=\"refinebad.png\" alt=\"Alternative text\" width=\"500\" align=\"center\"/>\n",
"\n",
"A solution is that elements of the green closure will not be further refined. \n",
"Instead, remove the green closure, and replace it by red refinement. \n",
"\n",
"![](refinegood.pdf)"
"<img src=\"refinegood.png\" alt=\"Alternative text\" width=\"500\" align=\"center\"/>"
]
},
{
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"\n",
"If there occurs an irregular node, then also the neighbor triangle must be refined.\n",
"\n",
"![](bisect.pdf)\n",
"<img src=\"bisect.png\" alt=\"Alternative text\" width=\"500\" align=\"center\"/>\n",
"\n",
"To ensure finite termination, one has to avoid cycles in the initial mesh. \n",
"This can be obtained by first sorting the edges (e.g., by length), end then, \n",
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22 changes: 11 additions & 11 deletions aposteriori/aposteriori.html

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