Reduced basis stabilization and post-processing for the virtual element method

TL;DR

This paper introduces a reduced basis approach to efficiently approximate virtual element basis functions, enhancing stabilization and post-processing techniques for improved computational performance.

Contribution

It proposes a novel reduced basis method for virtual element basis functions, aiding stabilization and post-processing in the virtual element method.

Findings

Reduced basis approximations are computationally efficient.

Enhanced stabilization improves solution accuracy.

Post-processing benefits from the reduced basis approach.

Abstract

We present a reduced basis method for cheaply constructing (possibly rough) approximations to the nodal basis functions of the virtual element space, and propose to use such approximations for the design of the stabilization term in the virtual element method and for the post-processing of the solution.