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Papers by Longlong Smith

Research paper thumbnail of A new finite element formulation for computational fluid dynamics: V. Circumventing the babu\vska-brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations

Computer Methods in Applied Mechanics and Engineering, 1986

A new Petrov-Galerkin formulation of the Stokes problem is proposed. The new formulation possesse... more A new Petrov-Galerkin formulation of the Stokes problem is proposed. The new formulation possesses better stability properties than the classical Galerkin/variational method. An error analysis is performed for the case in which both the velocity and pressure are approximated by C0 interpolations. Combinations of C0 interpolations which are unstable according to the Babuška-Brezzi condition (e.g., equal-order interpolations) are shown to be stable and convergent within the present framework. Calculations exhibiting the good behavior of the methodology are presented.

Research paper thumbnail of An introduction to computational fluid dynamics - the finite volume method

Research paper thumbnail of Computational Fluid Dynamics

Mathematics of Computation, 1976

Research paper thumbnail of A new finite element formulation for computational fluid dynamics: V. Circumventing the babu\vska-brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations

Computer Methods in Applied Mechanics and Engineering, 1986

A new Petrov-Galerkin formulation of the Stokes problem is proposed. The new formulation possesse... more A new Petrov-Galerkin formulation of the Stokes problem is proposed. The new formulation possesses better stability properties than the classical Galerkin/variational method. An error analysis is performed for the case in which both the velocity and pressure are approximated by C0 interpolations. Combinations of C0 interpolations which are unstable according to the Babuška-Brezzi condition (e.g., equal-order interpolations) are shown to be stable and convergent within the present framework. Calculations exhibiting the good behavior of the methodology are presented.

Research paper thumbnail of An introduction to computational fluid dynamics - the finite volume method

Research paper thumbnail of Computational Fluid Dynamics

Mathematics of Computation, 1976

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