The conforming virtual element method for polyharmonic problems
This work provides a theoretical foundation for using virtual element methods to solve high-order differential problems, which is incremental for the numerical analysis community.
The authors develop and analyze a conforming virtual element method for polyharmonic boundary value problems, proving convergence in the energy norm.
In this work, we exploit the capability of virtual element methods in accommodating approximation spaces featuring high-order continuity to numerically approximate differential problems of the form $Δ^p u =f$, $p\ge1$. More specifically, we develop and analyze the conforming virtual element method for the numerical approximation of polyharmonic boundary value problems, and prove an abstract result that states the convergence of the method in the energy norm.