Anisotropic mesh generation methods based on ACVT and natural metric for anisotropic elliptic equation
Anisotropic meshes are known to be well-suited for problems which exhibit anisotropic solution features. Defining an appropriate metric tensor and designing an efficient algorithm for anisotropic mesh generation are two important aspects of the anisotropic mesh methodology. In this paper, we are con...
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| Veröffentlicht in: | Science China. Mathematics 2013-12, Vol.56 (12), p.2615-2630 |
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| creator | Huang, YunQing Su, YiFan Wei, HuaYi Yi, NianYu |
| description | Anisotropic meshes are known to be well-suited for problems which exhibit anisotropic solution features. Defining an appropriate metric tensor and designing an efficient algorithm for anisotropic mesh generation are two important aspects of the anisotropic mesh methodology. In this paper, we are concerned with the natural metric tensor for use in anisotropic mesh generation for anisotropic elliptic problems. We provide an algorithm to generate anisotropic meshes under the given metric tensor. We show that the inverse of the anisotropic diffusion matrix of the anisotropic elliptic problem is a natural metric tensor for the anisotropic mesh generation in three aspects: better discrete algebraic systems, more accurate finite element solution and superconvergence on the mesh nodes. Various numerical examples demonstrating the effectiveness are presented. |
| doi_str_mv | 10.1007/s11425-013-4728-4 |
| format | Article |
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Various numerical examples demonstrating the effectiveness are presented.</description><subject>Algorithms</subject><subject>Anisotropy</subject><subject>Applications of Mathematics</subject><subject>Finite element method</subject><subject>Inverse</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mesh generation</subject><subject>Tensors</subject><issn>1674-7283</issn><issn>1006-9283</issn><issn>1869-1862</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNqNkT1vwyAQhq2qlRql-QHdPHah5QwGPEZRv6RIXdKuCGNIHCXggD303xfXlbq1QQKO43lPp3uz7BbwPWDMHyIALUqEgSDKC4HoRTYDwSqUjuIyxYxTlD7IdbaIcY_TIhWmnMwyu3Rt9H3wXavzo4m7fGucCapvvUvvfuebmNcqmiZPieXqY5Mr1-RO9UNQh5EISWh9SOnfQuZwaLt-DE7Dd6mb7MqqQzSLn3uevT89blYvaP32_LparpGmBe4RIbTBddXUoCiplRaVFRWzDacgQDGmwGJbgjI1MKN1YUsqwJQgCDNGK0Hm2d1Utwv-NJjYy2MbdWpHOeOHKNMkeAWMcDgHhZLjktP_0ZIxkTbgM9AScEVZQRIKE6qDjzEYK7vQHlX4lIDl6KucfJXJVzn6KsdOikkTE-u2Jsi9H4JLI_1D9AV96aU5</recordid><startdate>20131201</startdate><enddate>20131201</enddate><creator>Huang, YunQing</creator><creator>Su, YiFan</creator><creator>Wei, HuaYi</creator><creator>Yi, NianYu</creator><general>Springer Berlin Heidelberg</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>KR7</scope><scope>7TG</scope><scope>KL.</scope></search><sort><creationdate>20131201</creationdate><title>Anisotropic mesh generation methods based on ACVT and natural metric for anisotropic elliptic equation</title><author>Huang, YunQing ; Su, YiFan ; Wei, HuaYi ; Yi, NianYu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c420t-334d0b9db1a43bac89f896fd74181a66a1f0f51aeb16ecc2f5481e51836eeca83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Algorithms</topic><topic>Anisotropy</topic><topic>Applications of Mathematics</topic><topic>Finite element method</topic><topic>Inverse</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mesh generation</topic><topic>Tensors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Huang, YunQing</creatorcontrib><creatorcontrib>Su, YiFan</creatorcontrib><creatorcontrib>Wei, HuaYi</creatorcontrib><creatorcontrib>Yi, NianYu</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><collection>Meteorological & Geoastrophysical Abstracts</collection><collection>Meteorological & Geoastrophysical Abstracts - Academic</collection><jtitle>Science China. 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| subjects | Algorithms Anisotropy Applications of Mathematics Finite element method Inverse Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Mesh generation Tensors |
| title | Anisotropic mesh generation methods based on ACVT and natural metric for anisotropic elliptic equation |
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