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Error Estimates in Balanced Norms of Finite Element Methods on Layer-Adapted Meshes for Second Order Reaction-Diffusion Problems Read chapter Read first chapter

2017 | OriginalPaper | Chapter

A DG Least-Squares Finite Element Method for Nagumo’s Nerve Equation with Fast Reaction: A Numerical Study

Author : Runchang Lin

Published in: Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016

Publisher: Springer International Publishing

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Abstract

The Nagumo equation is a simple nonlinear reaction-diffusion equation, which has important applications in neuroscience and biological electricity. If the equation is reaction-dominated, numerical oscillations may appear near the traveling wave front, which makes it challenging to find stable solutions. In the present study, a new method is developed on uniform meshes to solve the Nagumo equation. Numerical results are given to demonstrate the performance of the algorithm. Convergence rates with respect to spatial and temporal discretization are obtained experimentally. Some properties of the nerve model are confirmed numerically.

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previous chapter Energy-Norm A Posteriori Error Estimates for Singularly Perturbed Reaction-Diffusion Problems on Anisotropic Meshes: Neumann Boundary Conditions
next chapter Local Projection Stabilization for Convection-Diffusion-Reaction Equations on Surfaces
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Metadata
Title
A DG Least-Squares Finite Element Method for Nagumo’s Nerve Equation with Fast Reaction: A Numerical Study
Author
Runchang Lin
Copyright Year
2017
Book
Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016

Print ISBN: 978-3-319-67201-4

Electronic ISBN: 978-3-319-67202-1

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-67202-1_12

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