feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

  • 1
    Electronic Resource
    Electronic Resource
    Numerical algorithms 7 (1994), S. 269-293 
    ISSN: 1572-9265
    Keywords: Mixed finite element methods ; quadrilaterals ; hexahedra ; differential geometry ; tensor calculus ; finite element methods ; finite difference methods ; partial differential equations ; 65N30 ; 65N06 ; 65N50 ; 53A45 ; 35J20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We describe a new family of discrete spaces suitable for use with mixed methods on certain quadrilateral and hexahedral meshes. The new spaces are natural in the sense of differential geometry, so all the usual mixed method theory, including the hybrid formulation, carries over to these new elements with proofs unchanged. Because transforming general quadrilaterals into squares introduces nonlinearity and because mixed methods involve the divergence operator, the new spaces are more complicated than either the corresponding Raviart-Thomas spaces for rectangles or corresponding finite element spaces for quadrilaterals. The new spaces are also limited to meshes obtained from a rectangular mesh through the application of a single global bilinear transformation. Despite this limitation, the new elements may be useful in certain topologically regular problems, where initially rectangular grids are deformed to match features of the physical region. They also illustrate the difficulties introduced into the theory of mixed methods by nonlinear transformations.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 835-849 
    ISSN: 0271-2091
    Keywords: non-linear first-order hyperbolic system ; collocation method ; upwinding ; thermal pipeline simulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Simulating thermal effects in pipeline flow involves solving a coupled non-linear system of first-order hyperbolic equations. The advection term has two large eigenvalues of opposite signs, corresponding to the propagation of high-speed sound waves, and one eigenvalue close to or even equal to zero, representing the much slower fluid flow velocity, which transports temperature. Standard collocation methods work well for isothermal flow in pipelines, but the stagnating eigenvalue causes difficulties when thermal effects are included. In a companion paper we formulate and analyse a new numerical method for the non-linear system which arises in thermal modelling. The new method applies to general coupled systems of non-linear first-order hyperbolic partial differential equations with one degenerate eigenvalue. In the present paper we focus on a linearized constant coefficient form of the thermal flow equations. This substantially simplifies presentation of the error analysis for the numerical scheme. We also include numerical results for the method applied to the fully non-linear system. Both the error analysis and the numerical experiments show that the difficulties that come from the application of standard collocation can be overcome by using upwinded piecewise constant functions for the degenerate component of the solution.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...