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Constraint Energy Minimizing Generalized Multiscale Finite Element Method for Convection Diffusion Equations with Inhomogeneous Boundary Conditions
- Publication Year :
- 2024
-
Abstract
- In this paper, we develop the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for convection-diffusion equations with inhomogeneous Dirichlet, Neumann and Robin boundary conditions, along with high-contrast coefficients. For time independent problems, boundary correctors $\mathcal{D}^m$ and $\mathcal{N}^{m}$ for Dirichlet, Neumann, and Robin conditions are designed. For time dependent problems, a scheme to update the boundary correctors is formulated. Error analysis in both cases is given to show the first-order convergence in energy norm with respect to the coarse mesh size $H$ and second-order convergence in $L^2-$norm, as verified by numerical examples, with which different finite difference schemes are compared for temporal discretization. Nonlinear problems are also demonstrated in combination with Strang splitting.<br />Comment: 36 pages.11 figures. Submitted to Journal of Computational Mathematics
- Subjects :
- Mathematics - Numerical Analysis
65M12, 65M15, 65N30
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2408.00304
- Document Type :
- Working Paper