Automatická hp-adaptivita na sítích s visícími uzly libovolné úrovně ve 3D

Kůs, Pavel

The thesis is concerned with theoretical and practical aspects of the hp- adaptive finite element method for solving elliptic and electromagnetic prob- lems described by partial differential equations in three spatial dimensions. Besides the standard element refinements, the hp-adaptivity allows indepen- dent adaptation of degrees of the polynomial approximation as well. This leads to exponentially fast convergence even for problems with singularities. The efficiency of the hp-adaptivity is enhanced even more by the ability of the algorithm to work with meshes with arbitrary-level hanging nodes. This generality, however, leads to great complexity of the implementation. There- fore, the thesis concentrates on the mathematical analysis of algorithms that have led to successful implementation of the method. In addition, the the- sis discusses the numerical integration in 3D and the implementation of the method itself. Finally, numerical results obtained by this new implemen- tation are presented. They confirm advantages of hp-adaptivity on meshes with arbitrary-level hanging nodes. 1

host :: přihlásit Digitální repozitář
		Hledej		Nový záznam		Nápověda		O repozitáři