Use of Asymptotics for New Dynamic Adapted Mesh Construction for Periodic Solutions with an Interior Layer of Reaction-Diffusion-Advection Equations

DOI10.1007/978-3-319-57099-0_10zbMath1368.65166OpenAlexW2606090243MaRDI QIDQ5274933

Egor Nikulin, V. T. Volkov, Dmitry V. Lukyanenko, Nikolai N. Nefedov

Publication date: 7 July 2017

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-57099-0_10

zbMATH Keywords

numerical examplea priori estimatesShishkin meshinterior layerreaction-diffusion-advection equationssingularly perturbed parabolic periodic problemsdynamic adapted mesh

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (8)

Asymptotic solution of the inverse problem for restoring the modular type source in Burgers' equation with modular advection ⋮ On the features of numerical solution of coefficient inverse problems for nonlinear equations of the reaction-diffusion-advection type with data of various types ⋮ Solving of the coefficient inverse problem for a nonlinear singularly perturbed two-dimensional reaction-diffusion equation with the location of moving front data ⋮ Asymptotic solution of coefficient inverse problems for Burgers-type equations ⋮ Asymptotic analysis of solving an inverse boundary value problem for a nonlinear singularly perturbed time-periodic reaction-diffusion-advection equation ⋮ Existence and stability of a front-type periodic solution of a two-component system of parabolic equations ⋮ Analytical-numerical approach to describing time-periodic motion of fronts in singularly perturbed reaction-advection-diffusion models ⋮ Asymptotic stability of a stationary solution of a multidimensional reaction-diffusion equation with a discontinuous source

Uses Software

• RODAS

Cites Work

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• Singularly perturbed parabolic problems with non-smooth data.
• Existence and asymptotic stability of periodic solutions with an interior layer of reaction-advection-diffusion equations
• Existence and stability of periodic contrast structures in the reaction-advection-diffusion problem
• Comparison Principle for Reaction-Diffusion-Advection Problems with Boundary and Internal Layers
• Numerical Analysis of a 2d Singularly Perturbed Semilinear Reaction-Diffusion Problem
• Some general implicit processes for the numerical solution of differential equations

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