The role of stabilization in the virtual element method: A survey
Lorenzo Mascotto
Abstract
The virtual element method was introduced 10 years ago, and has generated a large number of theoretical results and applications ever since. Here, we overview the main mathematical results concerning the stabilization of the method as an introduction for newcomers in the field. In particular, we summarize the proofs of some results for two dimensional “nodal” conforming and nonconforming virtual element spaces to pinpoint the essential tools used in the stability analysis. We discuss their extensions to several other virtual elements. Finally, we show several ways to prove the interpolation estimates, including a recent one that is based on employing the stability bounds.
Topics & Concepts
Element (criminal law)Mathematical proofStability (learning theory)Interpolation (computer graphics)MathematicsField (mathematics)Calculus (dental)Computer scienceTheoretical computer scienceApplied mathematicsAlgorithmAlgebra over a fieldComputer graphics (images)Pure mathematicsGeometryMachine learningMedicineAnimationLawDentistryPolitical scienceAdvanced Numerical Methods in Computational MathematicsElectromagnetic Simulation and Numerical MethodsNumerical methods in engineering