Abstract
This work deals with the a posteriori error estimates for the Darcy–Forchheimer problem. We first introduce the corresponding variational formulation for the nonlinear problem and discretize it by using the finite-element method. We then propose a linear iterative scheme to solve the nonlinear variational problem for a fixed mesh step. Finally, a posteriori error estimate with two types of computable error indicators is showed. The first one is linked to the linearization and the second one to the discretization. Numerical computations are performed to show the effectiveness of the derived error indicators.
Funding source: Agence Nationale de la Recherche
Award Identifier / Grant number: ANR-17-CE40-0029
Funding statement: Faouzi Triki was supported by the grant ANR-17-CE40-0029 of the French National Research Agency ANR (project MultiOnde.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Recent Advances in Boundary Element Methods
- Fast Barrier Option Pricing by the COS BEM Method in Heston Model (with Matlab Code)
- Bernoulli Free Boundary Problems Under Uncertainty: The Convex Case
- CVEM-BEM Coupling for the Simulation of Time-Domain Wave Fields Scattered by Obstacles with Complex Geometries
- Developments on the Stability of the Non-symmetric Coupling of Finite and Boundary Elements
- Coupling of Finite and Boundary Elements for Singularly Nonlinear Transmission and Contact Problems
- BEM-Based Magnetic Field Reconstruction by Ensemble Kálmán Filtering
- Force Computation for Dielectrics Using Shape Calculus
- A Time-Adaptive Space-Time FMM for the Heat Equation
- Integral Representations and Quadrature Schemes for the Modified Hilbert Transformation
- High-Order Compact Finite Difference Methods for Solving the High-Dimensional Helmholtz Equations
- A Posteriori Error Estimates for Darcy–Forchheimer’s Problem
- Convergence of a Finite Difference Scheme for a Flame/Smoldering-Front Evolution Equation and Its Application to Wavenumber Selection
Articles in the same Issue
- Frontmatter
- Recent Advances in Boundary Element Methods
- Fast Barrier Option Pricing by the COS BEM Method in Heston Model (with Matlab Code)
- Bernoulli Free Boundary Problems Under Uncertainty: The Convex Case
- CVEM-BEM Coupling for the Simulation of Time-Domain Wave Fields Scattered by Obstacles with Complex Geometries
- Developments on the Stability of the Non-symmetric Coupling of Finite and Boundary Elements
- Coupling of Finite and Boundary Elements for Singularly Nonlinear Transmission and Contact Problems
- BEM-Based Magnetic Field Reconstruction by Ensemble Kálmán Filtering
- Force Computation for Dielectrics Using Shape Calculus
- A Time-Adaptive Space-Time FMM for the Heat Equation
- Integral Representations and Quadrature Schemes for the Modified Hilbert Transformation
- High-Order Compact Finite Difference Methods for Solving the High-Dimensional Helmholtz Equations
- A Posteriori Error Estimates for Darcy–Forchheimer’s Problem
- Convergence of a Finite Difference Scheme for a Flame/Smoldering-Front Evolution Equation and Its Application to Wavenumber Selection