A New Error Analysis of Characteristics-Mixed FEMs for Miscible Displacement in Porous Media
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Bibliographic record
Abstract
The method of characteristics type is especially effective for convection-dominated diffusion problems. Due to the nature of characteristic temporal discretization, the method allows one to use a large time step in many practical computations, while all previous theoretical analyses always required certain restrictions on the time stepsize. Here, we present a new analysis to establish unconditionally optimal error estimates for a modified method of characteristics with a mixed finite element approximation to the miscible displacement problem in $\mathbb{R}^d\ (d=2,3)$. For this purpose, we introduce a new characteristic time-discrete system. We prove that the $L^2$ error bound the characteristic time-discrete systemof the fully discrete method of characteristics to the time-discrete system is $\tau$-independent and the numerical solution is bounded in $W^{1,\infty}$-norm unconditionally. With the boundedness, optimal error estimates are established in a traditional manner. Numerical results confirm our theoretical analysis and clearly show the unconditional stability.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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