Analysis of Stabilized Finite Volume Method for Poisson Equation

Abstract

In this work, we systematically analyze a stabilized finite volume method for the Poisson equation. On stating the convergence of this method, optimal error estimates in different norms are obtained by establishing the adequate connections between the finite element and finite volume methods. Furthermore, some super-convergence results are established by using L ² -projection method on a coarse mesh based on some regularity assumptions for Poisson equation. Finally, some numerical experiments are presented to confirm the theoretical findings.

Keywords:

• Poisson equation
• finite volume method
• projection method
• superconvergence

AMS Subject Classification:

• 65M08
• 65N12
• 35J05