High-order accurate time-stepping schemes for convection-diffusion problems
نویسندگان
چکیده
منابع مشابه
High-order Time-accurate Schemes for Singularly Perturbed Parabolic Convection-diffusion Problems with Robin Boundary Conditions
The boundary-value problem for a singularly perturbed parabolic PDE with convection is considered on an interval in the case of the singularly perturbed Robin boundary condition; the highest space derivatives in the equation and in the boundary condition are multiplied by the perturbation parameter ε. In contrast to the Dirichlet boundary-value problem, for the problem under consideration the e...
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We consider the first boundary value problem for a singularly perturbed parabolic PDE with convection on an interval. For the case of sufficiently smooth data, it is easy to construct a standard finite difference operator and a piecewise uniform mesh, condensing in the boundary layer, which gives an ε-uniformly convergent difference scheme. The order of convergence for such a scheme is exactly ...
متن کاملModelling, Analysis and Simulation High-order time-accurate schemes for singularly perturbed parabolic convection-diffusion problems with Robin boundary conditions
The boundary value problem for a singularly perturbed parabolic PDE with convection is considered on an interval in the case of the singularly perturbed Robin boundary condition; the highest space derivatives in the equation and in the boundary condition are multiplied by the perturbation parameter ε. In contrast to a Dirichlet boundary value problem, for the problem under consideration the err...
متن کاملNovel Defect-correction High-order, in Space and Time, Accurate Schemes for Parabolic Singularly Perturbed Convection-diffusion Problems
New high-order accurate finite difference schemes based on defect correction are considered for an initial boundary-value problem on an interval for singularly perturbed parabolic PDEs with convection; the highest space derivative in the equation is multiplied by the perturbation parameter ε, ε ∈ (0, 1]. Solutions of the well-known classical numerical schemes for such problems do not converge ε...
متن کاملAcceleration by Parallel Computations of Solving High-Order Time-Accurate Difference Schemes for Singularly Perturbed Convection-Diffusion Problems
For singularly perturbed convection-diffusion problems with the perturbation parameter εmultiplying the highest derivatives, we construct a scheme based on the defect correction method and its parallel variant that converge ε-uniformly with second-order accuracy in the time variable. We also give the conditions under which the parallel computation accelerates the solution process with preservin...
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ژورنال
عنوان ژورنال: Computer Methods in Applied Mechanics and Engineering
سال: 2000
ISSN: 0045-7825
DOI: 10.1016/s0045-7825(99)00193-0