Abstract

Sixth-order partial differential systems arise in several applications involving complex physical phenomena. In this work, we develop virtual element schemes for the numerical solution of time-dependent sixth-order problems in two dimensions, considering both simply supported and Cahn-Hilliard-type boundary conditions. Using the Ciarlet-Raviart method, we write a variational formulation for the steady-state version in the Sobolev product space H2 x H1. Then, the resulting system is discretized by using a coupling of the enhanced C1-and C0-conforming virtual element approaches. The well-posedness analysis is developed through the Lax-Milgram Lemma, and under standard assumptions of the computational domain, we derive optimal error estimates for the main and auxiliary variables. Finally, we report a set of numerical experiments on different families of polygonal meshes to validate our theoretical results and illustrate the behavior and flexibility of the proposed numerical schemes.