A uniformly convergent scheme on a nonuniform mesh for convection-diffusion parabolic problems

By C. Clavero, J. C. Jorge, Francisco Javier Lisbona. 2003

138 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1d564254685763d78f446109182c9bfbb4f05ee6

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters (2015, methodology): “[4, 16], the use of a priori refined meshes is suggested to capture the solution behavior in the boundary layers numerically.”
A uniformly convergent B-spline collocation method on a nonuniform mesh for singularly perturbed one-dimensional time-dependent linear convection-diffusion problem (2008, methodology): “[2] give a uniform convergent numerical method with respect to the diffusion parameter to solve the one-dimensional time-dependent convection–diffusion problem.”
High‐order numerical methods for one‐dimensional parabolic singularly perturbed problems with regular layers (2005, background): “Assuming certain smoothness and compatibility requirements on s and f , in [18] the authors give the details to obtain these bounds for 0 ≤ j ≤ 3 when the Euler implicit rule is considered.”
A higher order difference method for singularly perturbed parabolic partial differential equations (2018, methodology): “Properties of continuous solution The continuous solution and its derivatives satisfy the following bounds, which can be shown by extending the analysis given in [5,24]: ∣∣∣ ∂p∂q ∂xp∂tq u(x, t) ∣∣∣ ≤ C(1 + ε−p exp (− αx/ε)), for (x, t) ∈ , and p + 2q ≤ 8, (4)”
Parameter-Robust Numerical Scheme for Time-Dependent Singularly Perturbed Reaction–Diffusion Problem with Large Delay (2018, background): “Awide variety of literature for the last two decades are based on the numerical solution of singularly perturbed parabolic partial di erential equations (SPPPDEs) with and without time delay [4, 8, 10, 13, 18, 19].”