Constraint Energy Minimizing Generalized Multiscale Finite Element Method for Convection Diffusion Equations with Inhomogeneous Boundary Conditions
<|reference_start|>Constraint Energy Minimizing Generalized Multiscale Finite Element Method for Convection Diffusion Equations with Inhomogeneous Boundary Conditions: 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.<|reference_end|>
@article{wong2024constraint,
    title={Constraint Energy Minimizing Generalized Multiscale Finite Element
  Method for Convection Diffusion Equations with Inhomogeneous Boundary
  Conditions},
    author={Po Chai Wong, Eric T. Chung, Changqing Ye, Lina Zhao},
    journal={arXiv preprint arXiv:2408.00304},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.00304},
    primaryClass={math.NA cs.NA}
}