Unconditional superconvergence analysis for nonlinear parabolic equation with \(EQ_1^{rot}\) nonconforming finite element
This paper studies the unconditional superconvergence analysis for a nonlinear parabolic equation on a bounded domain with a linearised Galerkin finite element method with \(EQ^{rot}_1\) nonconforming elements. Via a time-discretised system the error is split into a temporal and spatial component. The authors obtain the superclose result of \(u\) in the broken \(H^1\)-norm due to the two special characteristic of the nonconforming \(EQ^{rot}_1\) elements. The first characteristic is that the associated finite element (FE) interpolation operator is identical to the traditional Ritz projection; the second is that the consistency error can be bounded by order \(O(h^2)\) (one order higher than the interpolation error) when the exact solution of the problem belongs to \(H^3(\Omega)\) where \(\Omega\) is the relevant domain. Furthermore, a different strategy is employed to reach the order of \(O(h^2 + \tau^2)\) rather than \(O(h + \tau^2)\) as per previous works. The analysis presented herein may be employed for other nonconforming FEs possessing the above two properties.
scientific article; zbMATH DE number 6690795