LEADER 03753nam 22006015 450 001 9910574858103321 005 20251113182346.0 010 $a3-031-04279-4 024 7 $a10.1007/978-3-031-04279-9 035 $a(MiAaPQ)EBC7013135 035 $a(Au-PeEL)EBL7013135 035 $a(CKB)23524785900041 035 $aEBL7013135 035 $a(AU-PeEL)EBL7013135 035 $a(PPN)269149767 035 $a(OCoLC)1333084080 035 $a(DE-He213)978-3-031-04279-9 035 $a(EXLCZ)9923524785900041 100 $a20220606d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAnisotropic hp-Mesh Adaptation Methods $eTheory, implementation and applications /$fby Vít Dolej?í, Georg May 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2022. 215 $a1 online resource (258 pages) 225 1 $aNe?as Center Series,$x2523-3351 300 $aDescription based upon print version of record. 311 08$aPrint version: Dolejsí, Vít Anisotropic Hp-Mesh Adaptation Methods Cham : Springer International Publishing AG,c2022 9783031042782 327 $aIntroduction -- Metric Based Mesh Representation -- Interpolation Error Estimates for Two Dimensions -- Interpolation Error Estimates for Three Dimensions -- Anisotropic Mesh Adaptation, h-Variant -- Anisotropic Mesh Adaptation Method, hp-Variant -- Framework of the Goal-Oriented Error Estimates -- Goal-Oriented Anisotropic Mesh Adaptation -- Implementation Aspects -- Applications. 330 $aMesh adaptation methods can have a profound impact on the numerical solution of partial differential equations. If devised and implemented properly, adaptation significantly reduces the size of the algebraic systems resulting from the discretization, while ensuring that applicable error tolerances are met. In this monograph, drawing from many years of experience, the authors give a comprehensive presentation of metric-based anisotropic hp-mesh adaptation methods. A large part of this monograph is devoted to the derivation of computable interpolation error estimates on simplicial meshes, which take into account the geometry of mesh elements as well as the anisotropic features of the interpolated function. These estimates are then used for the optimization of corresponding finite element spaces in a variety of settings. Both steady and time dependent problems are treated, as well as goal-oriented adaptation. Practical aspects of implementation are also explored, including several algorithms. Many numerical experiments using the discontinuous Galerkin method are presented to illustrate the performance of the adaptive techniques. This monograph is intended for scientists and researchers, including doctoral and master-level students. Portions of the text can also be used as study material for advanced university lectures concerning a posteriori error analysis and mesh adaptation. 410 0$aNe?as Center Series,$x2523-3351 606 $aNumerical analysis 606 $aMathematics$xData processing 606 $aNumerical Analysis 606 $aComputational Science and Engineering 615 0$aNumerical analysis. 615 0$aMathematics$xData processing. 615 14$aNumerical Analysis. 615 24$aComputational Science and Engineering. 676 $a515.353 676 $a518 700 $aDolejs?i?$b Vi?t$0755608 702 $aMay$b Georg 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910574858103321 996 $aAnisotropic hp-Mesh adaptation methods$92997445 997 $aUNINA