An adaptive finite element method with crosswind diffusion for low Mach, steady, laminar combustion
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A coupled problem arising in induction heating furnaces is studied. The thermal problem, which involves a change of phase, has a nonlocal radiation boundary condition. Convective heat transfer in the liquid is also included which makes necessary to compute ...
Engineers rely on efficient simulations that provide them with reliable data in order to make proper engineering design decisions. The purpose of this thesis is to design adaptive numerical methods for multiscale problems in this spirit. We consider ellipt ...
A space–time adaptive method is presented for the numerical simulation of mass transport in electroosmotic and pressure-driven microflows in two space dimensions. The method uses finite elements with large aspect ratio, which allows the electroosmotic flow ...
An anisotropic a posteriori error estimate is derived for a finite element discretization of the wave equation in two space dimensions. Only the error due to space discretization is considered, and the error estimates are derived in the nonnatural L-2(0, T ...
The dynamic response of angle-ply laminated composite plates traversed by a moving mass or a moving force is investigated. For this purpose, a finite element method based on the first-order shear deformation theory is used. Stationary and adaptive mesh tec ...
In this paper we derive two a posteriori upper bounds for the heat equation. A continuous, piecewise linear finite element discretization in space and the Crank-Nicolson method for the time discretization are used. The error due to the space discretization ...
The purpose of this thesis is to investigate methods for the solution of multiscale problems both from the mathematical and numerical point of view, with a particular concern on applications to flows through heterogeneous porous media. After an overview of ...
We develop a discretisation and solution technique for elliptic problems whose solutions may present strong variations, singularities, boundary layers and oscillations in localised regions. We start with a coarse finite element discretisation with a mesh s ...
Theoretical and numerical aspects of multi-scale problems are investigated. On one hand, mathematical analysis is done on a new method for numerically solving problems with multi-scale behavior using multiple levels of not necessarily nested grids. A parti ...
We develop a discretization and solution technique for elliptic problems whose solutions may present strong variations, singularities, boundary layers and oscillations in localized regions. We start with a coarse finite element discretization with a mesh s ...