An Adaptive Characteristic Petrov-Galerkin Finite Element Method for Convection-Dominated Linear and Nonlinear Parabolic Problems in One Space Variable
نویسنده
چکیده
A new adaptive finite element method for convection-dominated problems is presented. A special feature of the method is that it is based on a Petrov-Galerkin scheme for spatial approximation at a typical time-step which employs test functions chosen so that the approximate solution coincides with the exact solution at the nodes of finite element grid. This procedure makes possible the derivation of /rul,l' local a posteriori error estimates and a very elTcctive solver. Numerical examples are discussed which illustrate the efficiency and elTcctively of the method. (;I 1986 Academic Pre ... Inc.
منابع مشابه
Finite Element Methods for Convection Diffusion Equation
This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...
متن کاملKrylov-Subspace Preconditioners for Discontinuous Galerkin Finite Element Methods
Standard (conforming) finite element approximations of convection-dominated convectiondiffusion problems often exhibit poor stability properties that manifest themselves as nonphysical oscillations polluting the numerical solution. Various techniques have been proposed for the stabilisation of finite element methods (FEMs) for convection-diffusion problems, such as the popular streamline upwind...
متن کاملHp-finite Element Methods for Hyperbolic Problems A
This paper is devoted to the a priori and a posteriori error analysis of the hp-version of the discontinuous Galerkin nite element method for partial differential equations of hyperbolic and nearly-hyperbolic character. We consider second-order partial diierential equations with nonnegative characteristic form, a large class of equations which includes convection-dominated diiusion problems , d...
متن کاملConvection-diffusion problems, SDFEM/SUPG and a priori meshes
This paper aims to give the reader a summary of current understanding of the streamlinediffusion finite element method (SDFEM), as applied to linear steady-state convection-diffusion problems. Towards this end, we begin with a brief description of the nature of convectiondiffusion problems: the structure of their solutions will be examined, with special emphasis on the main phenomena of exponen...
متن کاملA Space-Time Petrov-Galerkin Certified Reduced Basis Method: Application to the Boussinesq Equations
We present a space-time certified reduced basis method for long-time integration of parametrized noncoercive parabolic equations with quadratic nonlinearity. We first consider a finite element discretization based on discontinuous Galerkin time integration and introduce associated Petrov-Galerkin space-time trialand test-space norms which yields optimal and asymptotically mesh independent stabi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006