A robust Petrov–Galerkin discretisation of convection–diffusion equations
نویسندگان
چکیده
منابع مشابه
A robust Petrov-Galerkin discretisation of convection-diffusion equations
A Petrov-Galerkin discretization is studied of an ultra-weak variational formulation of the convection-diffusion equation in mixed form. To arrive at an implementable method, the truly optimal test space has to be replaced by its projection onto a finite dimensional test search space. To prevent that this latter space has to be taken increasingly large for vanishing diffusion, a formulation is ...
متن کاملA step towards holistic discretisation of stochastic partial differential equations
The long term aim is to use modern dynamical systems theory to derive discretisations of noisy, dissipative partial differential equations. As a first step we here consider a small domain and apply stochastic centre manifold techniques to derive a model. The approach automatically parametrises subgrid scale processes induced by spatially distributed stochastic noise. It is important to discreti...
متن کاملPoint-wise Integrated-RBF-based Discretisation of Differential Equations
This paper discusses a discretisation scheme which is based on point collocation and integrated radial basis function networks (IRBFNs) for the solution of elliptic differential equations (DEs). The use of IRBFNs to represent the field variable in a given DE gives several advantages over the case of using conventional RBFNs and polynomials. Some numerical examples are included for demonstration...
متن کاملConvergence of a Time Discretisation for Doubly Nonlinear Evolution Equations of Second Order
The convergence of a time discretisation with variable time steps is shown for a class of doubly nonlinear evolution equations of second order. This also proves existence of a weak solution. The operator acting on the zero-order term is assumed to be the sum of a linear, bounded, symmetric, strongly positive operator and a nonlinear operator that fulfills a certain growth and a Hölder-type cont...
متن کاملAccurate Discretisation of a Nonlinear Micromagnetic Problem
In this paper we propose a finite element discretization of the Maxwell-Landau-Lifchitz-Gilbert equations governing the electromagnetic field in a ferromagnetic material. Our point of view is that it is desirable for the discrete problem to possess conservation properties similar to the continuous system. We first prove the existence of a new class of Liapunov functions for the continuous probl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2014
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2014.06.019