Convergence Analysis of a Finite Volume Gradient Scheme for a Linear Parabolic Equation Using Characteristic Methods

The first aim of this work is to establish a finite volume scheme using the Characteristic method for non-stationary advection-diffusion equations. The second aim is to analyze the convergence order of this scheme. The finite volume method considered here has been developed recently in [3] to approximate heterogeneous and anisotropic diffusion problems using a general class of nonconforming meshes. The formulation of schemes using the finite volume method of [3] can be obtained by replacing the gradient of the exact solution by a stable and consistent discrete gradient. This work is a continuation of the previous ones [1, 2] in which we derived directly a finite volume scheme for the heat equation along with a convergence analysis.

Fayssal Benkhaldoun (1) , Abdallah Bradji (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 UBMA - Université Badji Mokhtar [Annaba]

Domaines: Analyse numérique [math.NA]

Fayssal Benkhaldoun, Abdallah Bradji. Convergence Analysis of a Finite Volume Gradient Scheme for a Linear Parabolic Equation Using Characteristic Methods. Large-Scale Scientific Computing, 11958, Springer International Publishing, pp.566-575, 2020, Lecture Notes in Computer Science, ⟨10.1007/978-3-030-41032-2_65⟩. ⟨hal-03872870⟩