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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
It is assumed that the interface cannot be fitted exactly.
📌 3 Key Takeaways
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Objective & Hypothesis:We present the solution of a second-order nonlinear parabolic interface problem on a quasiuniform triangular finite element with a linearized four-step implicit scheme used for the time discretization.
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Key Findings & Data:The convergence of the scheme in $L^2$-norm is established under certain regularity assumptions using interpolation and elliptic projection operators.
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Conclusion & Impact:It is assumed that the interface cannot be fitted exactly.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Four-step implicit · interface · almost-optimal
Abstract
We present the solution of a second-order nonlinear parabolic interface problem on a quasiuniform triangular finite element with a linearized four-step implicit scheme used for the time discretization. The convergence of the scheme in $L^2$-norm is established under certain regularity assumptions using interpolation and elliptic projection operators. A numerical experiment is presented to support the theoretical result. It is assumed that the interface cannot be fitted exactly.
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Cite This Article
ADEWOLE, M. O., PAYNE, V. F. (2018). Linearized four-step implicit scheme for nonlinear parabolic interface problems. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 6, 3034–3049. https://ajindex.com/articles/227817