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Monotone Finite Difference Schemes for Quasilinear Parabolic Problems with Mixed Boundary Conditions
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Francisco José Gaspar
,
Francisco Javier Lisbona
Published/Copyright:
January 20, 2016
Abstract
In this paper, we consider finite difference methods for two-dimensional quasilinear parabolic problems with mixed Dirichlet–Neumann boundary conditions. Some strong two-side estimates for the difference solution are provided and convergence results in the discrete norm are proved. Numerical examples illustrate the good performance of the proposed numerical approach.
Keywords: Two-Dimensional Quasilinear Parabolic Equation; Finite Difference Schemes; Monotonicity; Maximum Principle; Convergence
Received: 2015-10-10
Revised: 2016-1-4
Accepted: 2016-1-11
Published Online: 2016-1-20
Published in Print: 2016-4-1
© 2016 by De Gruyter
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Keywords for this article
Two-Dimensional Quasilinear Parabolic Equation;
Finite Difference Schemes;
Monotonicity;
Maximum Principle;
Convergence
Articles in the same Issue
- Frontmatter
- Vertex-Based Compatible Discrete Operator Schemes on Polyhedral Meshes for Advection-Diffusion Equations
- Reliable Averaging for the Primal Variable in the Courant FEM and Hierarchical Error Estimators on Red-Refined Meshes
- Monotone Finite Difference Schemes for Quasilinear Parabolic Problems with Mixed Boundary Conditions
- The Laguerre Collocation Method for Third Kind Integral Equations on Unbounded Domains
- Projection Methods for Ill-Posed Problems Revisited
- Explicit Constants in Poincaré-Type Inequalities for Simplicial Domains and Application to A Posteriori Estimates
- Regularization by Aggregation of Global and Local Data on the Sphere
- A Note on Lower Bounds of Eigenvalues of Fourth Order Elliptic Operators on Local Quasi-Uniform Grids
- Numerical Analysis and Computation of a Type of IMEX Method for the Time-Dependent Natural Convection Problem
- The Valuation of Carbon Bonds Linked with Carbon Price
