The finite element solution of a generalized Stokes system in terms of the flow variables stream function and vorticity is studied. This system results from a time discretization of the time-dependent Stokes system in...The finite element solution of a generalized Stokes system in terms of the flow variables stream function and vorticity is studied. This system results from a time discretization of the time-dependent Stokes system in stream function-vorticity formulation, or yet by the application of the characteristics method to solve the Navier-Stokes equations in the same representation. Numerical results presented for both cases illustrate the good behaviour of the adopted approach.展开更多
One of the reasons for the great success of the finite element method is its versatility to deal with different types of geometries. This is particularly true of problems posed in curved domains. Nevertheless it is we...One of the reasons for the great success of the finite element method is its versatility to deal with different types of geometries. This is particularly true of problems posed in curved domains. Nevertheless it is well-known that, for standard variational formulations, the optimal approximation properties known to hold for polytopic domains are lost, if meshes consisting of ordinary elements are still used in the case of curved domains. That is why method’s isoparametric version for meshes consisting of curved triangles or tetrahedra has been widely employed, especially in case Dirichlet boundary conditions are prescribed all over a curved boundary. However, besides geometric inconveniences, the isoparametric technique helplessly requires the manipulation of rational functions and the use of numerical integration. In this work we consider a simple alternative that bypasses these drawbacks, without eroding qualitative approximation properties. More specifically we work with a variational formulation leading to high order finite element methods based only on polynomial algebra, since they do not require the use of curved elements. Application of the new approach to Lagrange methods of arbitrary order illustrates its potential to take the best advantage of finite-element discretizations in the solution of wide classes of problems posed in curved domains.展开更多
Discontinuous Galerkin methods as a solution technique of second order elliptic problems,have been increasingly exploited by several authors in the past ten years.It is generally claimed the alledged attractive geomet...Discontinuous Galerkin methods as a solution technique of second order elliptic problems,have been increasingly exploited by several authors in the past ten years.It is generally claimed the alledged attractive geometrical flexibility of these methods,although they involve considerable increase of computational effort,as compared to continuous methods.This work is aimed at proposing a combination of DGM and non-conforming finite element methods to solve elliptic m-harmonic equations in a bounded domain of R^(n),for n=2 or n=3,with m≥n+1,as a valid and reasonable alternative to classical finite elements,or even to boundary element methods.展开更多
文摘The finite element solution of a generalized Stokes system in terms of the flow variables stream function and vorticity is studied. This system results from a time discretization of the time-dependent Stokes system in stream function-vorticity formulation, or yet by the application of the characteristics method to solve the Navier-Stokes equations in the same representation. Numerical results presented for both cases illustrate the good behaviour of the adopted approach.
文摘One of the reasons for the great success of the finite element method is its versatility to deal with different types of geometries. This is particularly true of problems posed in curved domains. Nevertheless it is well-known that, for standard variational formulations, the optimal approximation properties known to hold for polytopic domains are lost, if meshes consisting of ordinary elements are still used in the case of curved domains. That is why method’s isoparametric version for meshes consisting of curved triangles or tetrahedra has been widely employed, especially in case Dirichlet boundary conditions are prescribed all over a curved boundary. However, besides geometric inconveniences, the isoparametric technique helplessly requires the manipulation of rational functions and the use of numerical integration. In this work we consider a simple alternative that bypasses these drawbacks, without eroding qualitative approximation properties. More specifically we work with a variational formulation leading to high order finite element methods based only on polynomial algebra, since they do not require the use of curved elements. Application of the new approach to Lagrange methods of arbitrary order illustrates its potential to take the best advantage of finite-element discretizations in the solution of wide classes of problems posed in curved domains.
基金They also gratefully acknowledge the financial support provided by CNPq,the Brazilian National Research Council,through grants 307996/2008-5 and 304518/2002-6.
文摘Discontinuous Galerkin methods as a solution technique of second order elliptic problems,have been increasingly exploited by several authors in the past ten years.It is generally claimed the alledged attractive geometrical flexibility of these methods,although they involve considerable increase of computational effort,as compared to continuous methods.This work is aimed at proposing a combination of DGM and non-conforming finite element methods to solve elliptic m-harmonic equations in a bounded domain of R^(n),for n=2 or n=3,with m≥n+1,as a valid and reasonable alternative to classical finite elements,or even to boundary element methods.
