Sökning: "heat equation"

Visar resultat 6 - 10 av 164 avhandlingar innehållade orden heat equation.

1. 6. On weak and strong convergence of numerical approximations of stochastic partial differential equations

   Författare :Fredrik Lindgren; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Additive noise; Cahn-Hilliard-Cook equation; Error estimate; Finite element; Hyperbolic equation; Parabolic equation; Rational approximation; Stochastic partial differential equation; Strong convergence; Truncation; Wiener process; Weak convergence; Weak convergence;

   Sammanfattning : This thesis is concerned with numerical approximation of linear stochastic partial differential equations driven by additive noise. In the first part, we develop a framework for the analysis of weak convergence and within this framework we analyze the stochastic heat equation, the stochastic wave equation, and the linearized stochastic Cahn-Hilliard, or the linearized Cahn-Hilliard-Cook equation. LÄS MER

3. 7. Approximating Stochastic Partial Differential Equations with Finite Elements: Computation and Analysis

   Författare :Andreas Petersson; Chalmers tekniska högskola; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Lévy process; Lyapunov equation; white noise; finite element method; multilevel Monte Carlo; Monte Carlo; multiplicative noise; asymptotic mean square stability; stochastic heat equation; covariance operator; weak convergence; generalized Wiener process; numerical approximation; stochastic wave equation; Stochastic partial differential equations;

   Sammanfattning : Stochastic partial differential equations (SPDE) must be approximated in space and time to allow for the simulation of their solutions. In this thesis fully discrete approximations of such equations are considered, with an emphasis on finite element methods combined with rational semigroup approximations. LÄS MER

4. 8. On Numerical Methods for the Diffusion Equation Subject to Non-Local Boundary Conditions

   Författare :Gunnar Ekolin; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; forward Euler method; backward Euler method; the Crank-Nicolson method; heat equation; Galerkin finite element methods; backward Euler method;

   Sammanfattning : In the first paper three different finite difference methods for solving the heat equation in one space dimension with boundary conditions containing integrals over the interior of the interval are considered. The schemes are based on the forward Euler, the backward Euler and the Crank-Nicolson methods. Error estimates are derived in maximum norm. LÄS MER

5. 9. Computer-Assisted Proofs and Other Methods for Problems Regarding Nonlinear Differential Equations

   Författare :Oswald Fogelklou; Warwick Tucker; Gunilla Kreiss; Piotr Zgliczynski; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; computer-assisted proof; numerical verification; viscous Burgers’ equation; enclosure; existence; nonlinear boundary value problems; Euler equations; inverse problem; bicubic spline; interval analysis; heat equation; fluid limit; peer-to-peer networks; fixed points; stability; global stability; Mathematics; Matematik;

   Sammanfattning : This PhD thesis treats some problems concerning nonlinear differential equations. In the first two papers computer-assisted proofs are used. The differential equations there are rewritten as fixed point problems, and the existence of solutions are proved. LÄS MER

7. 10. Numerical Simulation of Turbulent Flows for Turbine Blade Heat Transfer Applications

   Författare :Jonas Larsson; Chalmers tekniska högskola; []
   Nyckelord :TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY; NATURVETENSKAP; NATURAL SCIENCES; k-.omega.; k-.epsilon.; explicit Runge-Kutta; finite volume; turbine; numerical method; non-linear; Navier-Stokes; supersonic; two-equation; external heat transfer; stagnation flow; two-dimensional; transition; low-Reynolds; turbulence model; impulse blade;

   Sammanfattning : Turbine blade heat transfer is an important engineering problem characterized by complex flow fields and high turbulence levels. This thesis is focused on using a full Navier-Stokes solver with two-equation eddy-viscosity models to predict external heat-transfer in single-stage, linear, two-dimensional uncooled turbine cascades. LÄS MER