Search for dissertations about: "galerkin"

Showing result 1 - 5 of 78 swedish dissertations containing the word galerkin.

2. 1. On discontinuous Galerkin multiscale methods

   Author : Daniel Elfverson; Axel Målqvist; Uppsala universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Beräkningsvetenskap med inriktning mot numerisk analys; Scientific Computing with specialization in Numerical Analysis;

   Abstract : In this thesis a new multiscale method, the discontinuous Galerkin multiscale method, is proposed. The method uses localized fine scale computations to correct a global coarse scale equation and thereby takes the fine scale features into account. READ MORE

4. 2. Multiscale Methods and Uncertainty Quantification

   Author : Daniel Elfverson; Axel Målqvist; Frédéric Legoll; Uppsala universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; multiscale methods; finite element method; discontinuous Galerkin; Petrov-Galerkin; a priori; a posteriori; complex geometry; uncertainty quantification; multilevel Monte Carlo; failure probability; Beräkningsvetenskap med inriktning mot numerisk analys; Scientific Computing with specialization in Numerical Analysis;

   Abstract : In this thesis we consider two great challenges in computer simulations of partial differential equations: multiscale data, varying over multiple scales in space and time, and data uncertainty, due to lack of or inexact measurements.We develop a multiscale method based on a coarse scale correction, using localized fine scale computations. READ MORE

5. 3. Automated Computational Modeling

   Author : Johan Jansson; Chalmers tekniska högskola; []
   Keywords : TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY; NATURVETENSKAP; NATURAL SCIENCES; multi-adaptivity; Galerkin; ODE; PDE; plasticity; elasticity; FEM; automated;

   Abstract : This thesis is part of the FEniCS project of Automation of Computational Mathematical Modeling (ACMM) as the modern manifestation of the basic principle of science:formulating mathematical equations (modeling) and solving equations (computation). The vision of FEniCS is to set a new standard towards the goals of generality, efficiency, and simplicity, concerning mathematical methodology, implementation, and application. READ MORE

6. 4. Valuing Path-Dependent Options using the Finite Element Method, Duality Techniques, and Model Reduction

   Author : Georgios Foufas; Göteborgs universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; finite element method; Galerkin; duality; a posteriori error estimation; adaptivity; option pricing; Greeks; Brownian motion; European option; barrier option; lookback option; Asian option; average option; POD; model reduction; balanced truncation; lookback option;

   Abstract : In this thesis we develop an adaptive finite element method for pricing of several path-dependent options including barrier options, lookback options, and Asian options. The options are priced using the Black-Scholes PDE-model, and the resulting PDE:s are of parabolic type in one spatial dimension with different boundary conditions and jump conditions at monitoring dates. READ MORE

7. 5. Adaptive variational multiscale methods

   Author : Axel Målqvist; Göteborgs universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; finite element method; Galerkin; duality; a posteriori error estimation; adaptivity; variational multiscale method; mixed formulation; multi-physics; oil reservoir simulation; finite element method;

   Abstract : In this thesis we present a new adaptive multiscale method for solving elliptic partial differential equations. The method is based on numerical solution of decoupled local fine scale problems on patches. READ MORE