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Superconvergence of Discontinuous Galerkin Methods for Convection-Diffusion Problems

Journal of Scientific Computing, 2009
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Zuozheng Zhang   +2 more
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Numerical techniques for solving convection-diffusion problems

1997
Many applied problems of continuum mechanics are connected with the necessity to solve problems of mass transfer induced not only by diffusion but convection too. Mathematical models of such processes are based on elliptic and parabolic equations with terms containing first-order derivatives.
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ℋ-matrices for Convection-diffusion Problems with Constant Convection

Computing, 2003
Hierarchical matrices provide a technique for the sparse approximation and matrix arithmetic of large, fully populated matrices. This technique has been proven to be applicable to matrices arising in the boundary and finite element method for uniformly elliptic operators with L∞-coefficients. This paper analyses the application of hierarchical matrices
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Solution of Degenerate Convection-Diffusion Problems by the Method of Characteristics

SIAM Journal on Numerical Analysis, 2001
The method of characteristics is developed for an initial boundary value problem for a degenerate convection-diffusion equation with mixed boundary condition. In the presented numerical scheme the convective terms are treated explicitely by the method of characteristics, while the diffusive terms are treated implicitely. In order to avoid degeneracy of
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A monotone Schwarz algorithm for a semilinear convection–diffusion problem

Journal of Numerical Mathematics, 2004
This paper deals with discrete monotone iterative algorithms for solving a nonlinear singularly perturbed convection-diffusion problem. A monotone domain decomposition algorithm based on a modification of a Schwartz alternating method is constructed. Numerical examples are also presented.
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A Robust Smoother for Convection-Diffusion Problems with Closed Characteristics

Computing, 2000
The author focusses attention on the robust property of a block Gauss-Seidel-type smoother. A downwind ordering is used in the inner part of the domain to obtain a lower triangular matrix for the discretization of the convection. The feedback introduced by the cyclic boundary conditions is handled by a block Gauss elimination.
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