LEADER 04586nam 22007695 450 001 9910300158803321 005 20200630054049.0 010 $a3-319-02663-1 024 7 $a10.1007/978-3-319-02663-3 035 $a(CKB)3710000000118064 035 $a(EBL)1730955 035 $a(OCoLC)884585383 035 $a(SSID)ssj0001244817 035 $a(PQKBManifestationID)11725413 035 $a(PQKBTitleCode)TC0001244817 035 $a(PQKBWorkID)11320470 035 $a(PQKB)10345160 035 $a(MiAaPQ)EBC1730955 035 $a(DE-He213)978-3-319-02663-3 035 $a(PPN)178785245 035 $a(EXLCZ)993710000000118064 100 $a20140522d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe Mimetic Finite Difference Method for Elliptic Problems /$fby Lourenco Beirao da Veiga, Konstantin Lipnikov, Gianmarco Manzini 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (399 p.) 225 1 $aMS&A, Modeling, Simulation and Applications,$x2037-5255 ;$v11 300 $aDescription based upon print version of record. 311 $a3-319-02662-3 320 $aIncludes bibliographical references and index. 327 $a1 Model elliptic problems -- 2 Foundations of mimetic finite difference method -- 3 Mimetic inner products and reconstruction operators -- 4 Mimetic discretization of bilinear forms -- 5 The diffusion problem in mixed form -- 6 The diffusion problem in primal form -- 7 Maxwells equations. 8. The Stokes problem. 9 Elasticity and plates -- 10 Other linear and nonlinear mimetic schemes -- 11 Analysis of parameters and maximum principles -- 12 Diffusion problem on generalized polyhedral meshes. 330 $aThis book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications. 410 0$aMS&A, Modeling, Simulation and Applications,$x2037-5255 ;$v11 606 $aComputer mathematics 606 $aMathematical physics 606 $aPartial differential equations 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006 615 0$aComputer mathematics. 615 0$aMathematical physics. 615 0$aPartial differential equations. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 14$aComputational Mathematics and Numerical Analysis. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aPartial Differential Equations. 615 24$aMathematical and Computational Engineering. 676 $a515.353 700 $aBeirao da Veiga$b Lourenco$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721660 702 $aLipnikov$b Konstantin$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aManzini$b Gianmarco$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300158803321 996 $aThe Mimetic Finite Difference Method for Elliptic Problems$92531403 997 $aUNINA