Adaptive multilevel methods for mortar edge element methods in IR_1hn3 [Elektronische Ressource] / vorgelegt von Werner Ernst Schabert

UNIVERSITMAUTILSAdaptive Multilevel Methods forMortar Edge Element Methods3in IRDissertationzur Erlangung des akademischen Titels einesDoktors der Naturwissenschaftender Mathematisch Naturwissenschaftlichen Fakult¨atder Universit¨at AugsburgLvorgelegt vonDipl. Phys. Werner Ernst SchabertIGAIUSGUSTANAE1. Gutachter: Prof. Dr. Ronald H.W. Hoppe2. Gutachter: Prof. Dr. Kunibert G. Siebert3. Gutachter: Prof. Dr. Jin-Fa LeeTag der mundlic¨ hen Prufung:¨ 9. Februar 2006AbstractThis thesis is concerned with the application of adaptive mortar edge elementmethods to the numerical solution of the quasi-stationary limit of Maxwellsequations, also known as the eddy current model, in three space dimensions.Althougheddycurrentmodelistime-dependent, werestrictouranalysistotime-independent problems that arise from a time discretization of the partial differ-ential equations.For the solution of these equations we consider the mortar approach, which re-lies on the macro-hybrid variational formulation of the problem with respect toa geometrically conforming, nonoverlapping decomposition of the computationaldomain (cf. [Hop99]). Based on independent, locally quasi-uniform and shaperegular simplicial triangulation of the subdomains we use the lowest order curl-conforming edge elements of N´ed´elec’s first family for the discretization of theproblem.