TY - JOUR

T1 - Petrov-Galerkin formulations with weighting functions dependent upon spatial and temporal discretization

T2 - Applications to transient convection-diffusion problems

AU - Tezduyar, I. E.

AU - Ganjoo, D. K.

N1 - Funding Information:
This researchw as sponsored by NASA under contract NAS-9-17380a nd by NSF under grant NSF MEA-8404810.W e are gratefulf or the computingr esourcesm ade availableb y the AerosciencesB ranch of the NASA Johnson Space Center.

PY - 1986/11

Y1 - 1986/11

N2 - A new Petrov-Galerkin finite element formulation has been proposed for transient convection-diffusion problems. Most Petrov-Galerkin formulations take into account the spatial discretization and the weighting functions so developed give satisfactory solutions for steady state problems. Though these schemes can be used for transient problems, there is scope for improvement. The schemes proposed here, which take into account temporal as well as spatial discretization, provide improved solutions. In view of the generality of the differential equation being solved, these schemes can be implemented for any physical problem which is governed by the transient convection-diffusion equation. It is also expected that these schemes, suitably adapted, will improve the numerical solutions of the compressible Euler and Navier-Stokes equations.

AB - A new Petrov-Galerkin finite element formulation has been proposed for transient convection-diffusion problems. Most Petrov-Galerkin formulations take into account the spatial discretization and the weighting functions so developed give satisfactory solutions for steady state problems. Though these schemes can be used for transient problems, there is scope for improvement. The schemes proposed here, which take into account temporal as well as spatial discretization, provide improved solutions. In view of the generality of the differential equation being solved, these schemes can be implemented for any physical problem which is governed by the transient convection-diffusion equation. It is also expected that these schemes, suitably adapted, will improve the numerical solutions of the compressible Euler and Navier-Stokes equations.

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U2 - 10.1016/0045-7825(86)90023-X

DO - 10.1016/0045-7825(86)90023-X

M3 - Article

AN - SCOPUS:0022810950

VL - 59

SP - 49

EP - 71

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

IS - 1

ER -