A comparative analysis of adaptive algorithms in the finite element method for solving the boundary value problem for a stationary reaction-diffusion equation

DOI10.3103/S0278641916030080zbMath1353.65084OpenAlexW2508626837MaRDI QIDQ344023

E. S. Nikolaev, N. D. Zolotareva

Publication date: 22 November 2016

Published in: Moscow University Computational Mathematics and Cybernetics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s0278641916030080

zbMATH Keywords

algorithmfinite element methodadaptive methodsnumerical experimentsingularly perturbed problemscorrection indicatorstationary reaction-diffusion equation

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Cites Work

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• Implementation and efficiency analysis of an adaptive \textit{hp}-finite element method for solving boundary value problems for the stationary reaction-diffusion equation
• Adaptive mesh refinement in boundary value problems for linear ODE systems
• Method for constructing meshes adapting to the solution of boundary value problems for ordinary differential equations of the second and fourth orders
• Adaptive \(hp\)-finite element method for solving boundary value problems for the stationary reaction-diffusion equation
• Stagnation in the \(p\)-version of the finite element method
• Adaptive \(p\)-version of the finite element method for solving boundary value problems for ordinary second-order differential equations
• A Posteriori Error Estimates Based on Hierarchical Bases

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