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- W4304091362 abstract "The time discrete scheme of characteristics type is especially effective for convection-dominated diffusion problems. The scheme has been used in various engineering areas with different approximations in spatial direction. The lowest-order mixed method is the most popular one for miscible flow in porous media. The method is based on a linear Lagrange approximation to the concentration and the zero-order Raviart-Thomas approximation to the pressure/velocity. However, the optimal error estimate for the lowest-order characteristics-mixed FEM has not been presented although numerous effort has been made in last several decades. In all previous works, only first-order accuracy in spatial direction was proved under certain time-step and mesh size restrictions. The main purpose of this paper is to establish optimal error estimates, $i.e.$, the second-order in $L^2$-norm for the concentration and the first-order for the pressure/velocity, while the concentration is more important physical component for the underlying model. For this purpose, an elliptic quasi-projection is introduced in our analysis to clean up the pollution of the numerical velocity through the nonlinear dispersion-diffusion tensor and the concentration-dependent viscosity. Moreover, the numerical pressure/velocity of the second-order accuracy can be obtained by re-solving the (elliptic) pressure equation at a given time level with a higher-order approximation. Numerical results are presented to confirm our theoretical analysis." @default.
- W4304091362 created "2022-10-10" @default.
- W4304091362 creator A5025671097 @default.
- W4304091362 date "2022-04-27" @default.
- W4304091362 modified "2023-09-27" @default.
- W4304091362 title "Analysis of lowest-order characteristics-mixed FEMs for incompressible miscible flow in porous media" @default.
- W4304091362 doi "https://doi.org/10.48550/arxiv.2204.12751" @default.
- W4304091362 hasPublicationYear "2022" @default.
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