Sökning: "Space-time variational problem"

Visar resultat 1 - 5 av 6 avhandlingar innehållade orden Space-time variational problem.

1. 1. Variational Methods for Moments of Solutions to Stochastic Differential Equations

   Författare :Kristin Kirchner; Chalmers tekniska högskola; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Additive and multiplicative noise; Stochastic partial differential equation; Projective and injective tensor product space; Hilbert tensor product space; Space-time variational problem; Petrov-Galerkin discretization; Stochastic ordinary differential equation;

   Sammanfattning : 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. LÄS MER

3. 2. A weak space-time formulation for the linear stochastic heat equation

   Författare :Matteo Molteni; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Inf-sup theory; Stochastic heat equation; Petrov-Galerkin; Finite element; Crank-Nicolson; Quasi-optimality; Finite element;

   Sammanfattning : 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. LÄS MER

4. 3. Numerical Approximation of Solutions to Stochastic Partial Differential Equations and Their Moments

   Författare :Kristin Kirchner; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Petrov– Galerkin discretizations; Strong and weak convergence; Fractional operators; Finite element methods; Space-time variational problems; Tensor product spaces; Stochastic partial differential equations; White noise; Petrov– Galerkin discretizations;

   Sammanfattning : 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. LÄS MER

5. 4. Automation of Computational Mathematical Modeling

   Författare :Anders Logg; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; computational mathematical modeling; automation; adaptivity; multi-adaptivity; individual time steps; dual problem; a priori; a posteriori; model reduction; individual time steps;

   Sammanfattning : This thesis concerns the Automation of Computational Mathematical Modeling (CMM), involving the key steps of automation of (i) discretization, (ii) discrete solution, (iii) error control, (iv) modeling, and (v) optimization. The automation of (i)--(ii) is realized through multi-adaptive Galerkin methods on general discretizations of space-time with time steps variable in space. LÄS MER

7. 5. On Error-Controlled Numerical Model Reduction for Linear Transient FE² Analysis

   Författare :Fredrik Ekre; Chalmers tekniska högskola; []
   Nyckelord :TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY; NATURVETENSKAP; NATURAL SCIENCES; computational homogenization; error estimation; model reduction;

   Sammanfattning : Multiscale modeling is of high interest in the engineering community due to its ability to capture the overall response, while still accounting for processes and structures on underlying fine scales. One standard approach to multiscale modeling is the so-called FE² procedure, where the classic constitutive relation is replaced by a boundary value problem on a Representative Volume Element (RVE) comprising the underlying microscale features. LÄS MER