LAUSR

Nonconforming quadrilateral EQ1rot finite element method (FEM) of nonlinear Kirchhoff‐type equation with damping is studied on anisotropic meshes. Based on the property of the nonlocal term of this equation, unconditional optimal error estimates of O(h) and O(h+τ2) ( h , the spatial parameter, and τ , the time step) in the broken H1 norm are deduced for the semidiscrete and a linearized fully discrete schemes without any restrictions of τ through a distinct approach compared with the methods used for other partial differential equations, respectively. Besides, the damping term appearing in the Kirchhoff‐type equation is solved with a novel technique, which is the major difficulty in the theoretical analysis. Finally, some numerical results are provided to verify the theoretical analysis.