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Stability and convergence analysis for a new phase field crystal model with a nonlocal Lagrange multiplier
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  • Shimin Lin,
  • Junying Cao,
  • Jun Zhang,
  • Tao Sun
Shimin Lin
Jimei University
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Junying Cao
Guizhou Minzu University
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Jun Zhang
Guizhou University of Finance and Economics
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Tao Sun
Shanghai Lixin University of Accounting and Finance
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Peer review status:UNDER REVIEW

25 Jun 2020Submitted to Mathematical Methods in the Applied Sciences
27 Jun 2020Assigned to Editor
27 Jun 2020Submission Checks Completed
27 Jun 2020Reviewer(s) Assigned

Abstract

In this work, an energy stable numerical scheme is proposed to solve the PFC model with a nonlocal Lagrange multiplier. The construction of the numerical scheme is based on invariant energy quadratization (IEQ) technique to transform a nonlinear system into a linear system, while the time variables is discretized by second order scheme. The stability term in the new scheme can balance the influence of nonlinear term. Moreover, we obtain the results of unconditional energy stability, uniqueness and uniform boundedness of numerical solution, and the numerical scheme is convergent with order of $\mathcal{O}(\delta t^2)$. Several numerical tests are conducted to confirm the theoretical results.