Search for dissertations about: "Petrov-Galerkin"
Showing result 1 - 5 of 11 swedish dissertations containing the word Petrov-Galerkin.
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1. Multiscale Methods and Uncertainty Quantification
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
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2. A weak space-time formulation for the linear stochastic heat equation
Abstract : The topic covered in this thesis is the introduction of a new formulation for the linear stochastic heat equation driven by additive noise, based on the space-time variational formulation for its deterministic counterpart. Having a variational formulation allows the use of the so called inf-sup theory in order to obtain results of existence and uniqueness in a relatively simple way. READ MORE
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3. The Dirac Equation: Numerical and Asymptotic Analysis
Abstract : The thesis consists of three parts, although each part belongs to a specific subject area in mathematics, they are considered as subfields of the perturbation theory. The main objective of the presented work is the study of the Dirac operator; the first part concerns the treatment of the spurious eigenvalues in the computation of the discrete spectrum. READ MORE
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4. Variational Methods for Moments of Solutions to Stochastic Differential Equations
Abstract : Numerical methods for stochastic differential equations typically estimate moments of the solution from sampled paths. Instead, we pursue the approach proposed by A. Lang, S. Larsson, and Ch. READ MORE
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5. Numerical Approximation of Solutions to Stochastic Partial Differential Equations and Their Moments
Abstract : The first part of this thesis focusses on the numerical approximation of the first two moments of solutions to parabolic stochastic partial differential equations (SPDEs) with additive or multiplicative noise. More precisely, in Paper I an earlier result (A. Lang, S. Larsson, and Ch. READ MORE