New approximate method for the Allen–Cahn equation with double-obstacle constraint and stability criteria for numerical simulations
| Autor: | Keisuke Takasao, Noriaki Yamazaki, Tomoyuki Suzuki |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Computer simulation
Multivalued function lcsh:Mathematics General Mathematics Mathematical analysis Interval (mathematics) lcsh:QA1-939 Stability (probability) Constraint (information theory) Euler method symbols.namesake Indicator function Allen-Cahn equation| constraint| double obstacle| stability| subdi erential| numerical simulations symbols Allen–Cahn equation Mathematics |
| Zdroj: | AIMS Mathematics, Vol 1, Iss 3, Pp 288-317 (2016) |
| ISSN: | 2473-6988 |
| DOI: | 10.3934/math.2016.3.288 |
| Popis: | In a numerical study, we consider the Allen–Cahn equation with a double-obstacle constraint. The constraint is a multivalued function that is provided by the subdi erential of the indicator function on a closed interval. Therefore, performing a numerical simulation of our problem poses diffculties. We propose a new approximate method for the constraint and demonstrate its validity. Moreover, we present stability criteria for the standard forward Euler method guaranteeing stable numerical experiments when using the approximating equation. |
| Databáze: | OpenAIRE |
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