|
| |
|
|
Numerical analysis of approximation of nonpolygonal domains for discontinuous Galerkin method
Klouda, Filip ; Dolejší, Vít (advisor) ; Sobotíková, Veronika (referee)
Title: Numerical analysis of approximation of nonpolygonal domains for discon- tinuous Galerkin method Author: Filip Klouda Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Vít Dolejší, Ph.D., DSc., KNM MFF UK Abstract: In this work we use the discontinuous Galerkin finite element method for the semidiscretization of a nonlinear nonstationary convection-diffusion pro- blem defined on a nonpolygonal two-dimensional domain. Using so called appro- ximating curved elements we define a piecewise polynomial approximation of the boundary of the domain and a space on which we search for a solution. We study the convergence of the method considering a symmetric as well as nonsymmetric discretization of diffusion terms and with the interior and boundary penalty. The obtained results allow us to derive an error estimate for the Discontinuous Galer- kin method employing the approximating curved elements. This estimate depends on the order of the approximation of the solution and also on the order of the approximation of the boundary. We describe one possibility of the construction of the approximating curved elements with the aid of a polynomial mapping given by an interpolation of points on the boundary. We present numerical experiments. Keywords: nonlinear convection-diffusion equation, discontinuous...
|
|
|
Numerical analysis of approximation of nonpolygonal domains for discontinuous Galerkin method
Klouda, Filip ; Dolejší, Vít (advisor)
Title: Numerical analysis of approximation of nonpolygonal domains for discon- tinuous Galerkin method Author: Filip Klouda Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Vít Dolejší, Ph.D., DSc., KNM MFF UK Abstract: In this work we use the discontinuous Galerkin finite element method for the semidiscretization of a nonlinear nonstationary convection-diffusion pro- blem defined on a nonpolygonal two-dimensional domain. Using so called appro- ximating curved elements we define a piecewise polynomial approximation of the boundary of the domain and a space on which we search for a solution. We study the convergence of the method considering a symmetric as well as nonsymmetric discretization of diffusion terms and with the interior and boundary penalty. The obtained results allow us to derive an error estimate for the Discontinuous Galer- kin method employing the approximating curved elements. This estimate depends on the order of the approximation of the solution and also on the order of the approximation of the boundary. We describe one possibility of the construction of the approximating curved elements with the aid of a polynomial mapping given by an interpolation of points on the boundary. We present numerical experiments. Keywords: nonlinear convection-diffusion equation, discontinuous...
|
|
|
Marketing of virtual reality: Case study of Oculus VR
Klouda, Filip ; Klabíková Rábová, Tereza (advisor) ; Klimeš, David (referee)
This thesis deals with the use of marketing communication for virtual reality devices from Oculus VR, which includes the Oculus Rift, Samsung Gear VR and Oculus Go. Main attention is drawn towards the Oculus Rift, which was the first commercially available VR device to render a fully 3D environment. The thesis analyzes various tools of marketing communication used in promoting the Rift and other Oculus products. The first part is devoted to theoretical concepts of virtual reality and the long history of this phenomenon, from the first stereoscope to modern head-mounted displays we know today. The following chapter examines the theories of marketing and public relations, as well as related concepts of digital marketing, event marketing and crisis communication. The second part presents the reader with an analysis of several forms of commercial communication used for promoting the Oculus Rift, including the crowdfunding campaign on Kickstarter, interacting with target audiences on social media and showcasing the Rift on various gaming and technology events. The closing part of the analysis provides the reader with an overview of the PR crisis the company faced in 2016 in relation to a political lobbying scandal of Oculus' founder Palmer Luckey.
|
|
|
Numerical analysis of approximation of nonpolygonal domains for discontinuous Galerkin method
Klouda, Filip ; Dolejší, Vít (advisor)
Title: Numerical analysis of approximation of nonpolygonal domains for discon- tinuous Galerkin method Author: Filip Klouda Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Vít Dolejší, Ph.D., DSc., KNM MFF UK Abstract: In this work we use the discontinuous Galerkin finite element method for the semidiscretization of a nonlinear nonstationary convection-diffusion pro- blem defined on a nonpolygonal two-dimensional domain. Using so called appro- ximating curved elements we define a piecewise polynomial approximation of the boundary of the domain and a space on which we search for a solution. We study the convergence of the method considering a symmetric as well as nonsymmetric discretization of diffusion terms and with the interior and boundary penalty. The obtained results allow us to derive an error estimate for the Discontinuous Galer- kin method employing the approximating curved elements. This estimate depends on the order of the approximation of the solution and also on the order of the approximation of the boundary. We describe one possibility of the construction of the approximating curved elements with the aid of a polynomial mapping given by an interpolation of points on the boundary. We present numerical experiments. Keywords: nonlinear convection-diffusion equation, discontinuous...
|
|
|
Numerical analysis of approximation of nonpolygonal domains for discontinuous Galerkin method
Klouda, Filip ; Dolejší, Vít (advisor) ; Sobotíková, Veronika (referee)
Title: Numerical analysis of approximation of nonpolygonal domains for discon- tinuous Galerkin method Author: Filip Klouda Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Vít Dolejší, Ph.D., DSc., KNM MFF UK Abstract: In this work we use the discontinuous Galerkin finite element method for the semidiscretization of a nonlinear nonstationary convection-diffusion pro- blem defined on a nonpolygonal two-dimensional domain. Using so called appro- ximating curved elements we define a piecewise polynomial approximation of the boundary of the domain and a space on which we search for a solution. We study the convergence of the method considering a symmetric as well as nonsymmetric discretization of diffusion terms and with the interior and boundary penalty. The obtained results allow us to derive an error estimate for the Discontinuous Galer- kin method employing the approximating curved elements. This estimate depends on the order of the approximation of the solution and also on the order of the approximation of the boundary. We describe one possibility of the construction of the approximating curved elements with the aid of a polynomial mapping given by an interpolation of points on the boundary. We present numerical experiments. Keywords: nonlinear convection-diffusion equation, discontinuous...
|
|
| |
guest ::
