Unconditionally Optimal Error Estimates of a Crank--Nicolson Galerkin Method for the Nonlinear Thermistor Equations
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Bibliographic record
Abstract
This paper focuses on unconditionally optimal error analysis of an uncoupled and linearized Crank-Nicolson Galerkin finite element method for the time-dependent nonlinear thermistor equations in <i>d</i>-dimensional space, <i>d</i> = 2, 3. In our analysis, we split the error function into two parts, one from the spatial discretization and one from the temporal discretization, by introducing a corresponding time-discrete (elliptic) system. We present a rigorous analysis for the regularity of the solution of the time-discrete system and error estimates of the time discretization. With these estimates and the proved regularity, optimal error estimates of the fully discrete Crank-Nicolson Galerkin method are obtained unconditionally. Numerical results confirm our analysis and show the efficiency of the method.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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