A Unified Analysis of Nonconforming Virtual Element Methods for Convection Diffusion Reaction Problem
This work addresses the challenge of stabilizing nonconforming virtual element methods for convection-dominated problems, which is important for computational fluid dynamics and related fields.
The paper analyzes nonconforming virtual element methods for convection-dominated convection-diffusion-reaction problems, showing that linear nonconforming VEM fails to converge and proposing a new SDFEM-type stabilized method that is stable in the vanishing diffusion limit.
We discuss nonconforming virtual element method for convection dominated (diffusive coefficient is very small compared to convective coefficient and reac- tion coefficient ) convection-diffusion-reaction equation using L^2 projection operator.In this paper we stabilize the stabilization terms using same technique which is used for stabilization of symmetric part in VEM, where T is an arbitrary element, and assume H^2(T) regularity on each element to prove polynomial consistency where v_h is approximate solution.We have shown that linear nonconforming VE is not convergent for convection dominated convection-diffusion reaction problem and higher regu larity of f ,source term is also needed for convergence analysis.The novelty of this paper is we introduce a new SDFEM type nonconforming virtual element method for convection-dominated convection diffusion reaction equation, and discuss the computability issue using degrees of freedom of element without explicit knowledge of basis functions of virtual element methods.The present framework is stable in the limit of vanishing diffusion.