Analysis of Lowest-Order Characteristics-Mixed FEMs for Incompressible Miscible Flow in Porous Media

نویسندگان

چکیده

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

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ژورنال

عنوان ژورنال: SIAM Journal on Numerical Analysis

سال: 2021

ISSN: ['0036-1429', '1095-7170']

DOI: https://doi.org/10.1137/20m1318766