Stable $$C^1$$-conforming finite element methods for a class of nonlinear fourth-order evolution equations

Abstract We propose $C^1$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msup mml:miC</mml:mi> mml:mn1</mml:mn> </mml:msup> </mml:math> -conforming finite element methods for a class of nonlinear fourth-order partial differential equations arising in continuum physics. Our primary motivation is the Landau–Lifshitz–Baryakhtar equation in micromagnetics, although the framework also applies to other fourth-order models such as the convective Swift–Hohenberg equation and Cahn–