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Monotone Discretizations for Elliptic Second Order Partial Differential Equations

This book offers a comprehensive presentation of numerical methods for elliptic boundary value problems that satisfy discrete maximum principles (DMPs). The satisfaction of DMPs ensures that numerical solutions possess physically admissible values, which is of utmost importance in numerous applicati...

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Bibliographic Details
Main Authors: Barrenechea, Gabriel R. (Author), John, Volker (Author), Knobloch, Petr (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Cham : Springer Nature Switzerland : Imprint: Springer, 2025.
Edition:1st ed. 2025.
Series:Springer Series in Computational Mathematics, 61
Subjects:
Mathematical analysis.
Mathematics > Data processing.
Analysis.
Computational Mathematics and Numerical Analysis.
Online Access:https://doi.org/10.1007/978-3-031-80684-1
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Table of Contents:
  • - Introduction. - Convection-Di usion-Reaction Problems and Maximum Principles
  • Discrete Maximum Principles
  • Partitions of the Domain
  • Finite Element Methods
  • Finite Element Methods for Diffusion Problems
  • Finite Element Methods for Reaction-Diffusion Problems
  • Linear Finite Element Methods for Convection-Diffusion-Reaction Problems
  • Nonlinear Finite Element Methods for Convection-Diffusion-Reaction Problems: Discretizations Based on Modi ed Variational Forms
  • Nonlinear Finite Element Methods for Convection-Diffusion-Reaction Problems: Algebraically Stabilized Methods
  • Finite Difference Methods
  • Finite Volume Methods
  • A Numerical Study for a Problem with Different Regimes
  • Outlook.

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