Numerical Analysis and Computation of a Type of IMEX Method for the Time-Dependent Natural Convection Problem
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Yun-Bo Yang
Abstract
A new numerical regularization method for the natural convection problem is presented, which is based on a type of implicit-explicit (IMEX) second-order time-stepping schemes in temporal discretization and stabilized mixed finite element in spatial discretization. This method deals with a non-linear advection term in both the momentum equation and the energy equation by linearization. We only need to solve a linear problem at each time step and the discrete curvature of the solutions is added as a stabilization term for the velocity, the pressure and the temperature, respectively. Unconditional stability is proved and an a priori error estimate is derived. Finally, a series of numerical experiments are also given to confirm the theoretical analysis and to demonstrate the efficiency of the new method.
Funding source: Natural Science Foundation of China
Award Identifier / Grant number: 11371287
The authors would like to thank the editor and the anonymous referees for their careful reading and their valuable comments which led to a great improvement of the present article.
© 2016 by De Gruyter
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
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
