Stability and convergence analysis for a new phase field crystal model
with a nonlocal Lagrange multiplier
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.