Error estimates for a finite volume element method for parabolic equations in convex polygonal domains.

*(English)*Zbl 1067.65092A parabolic problem in a bounded, convex polygonal domain in the plane is considered.

Some details about error estimates for the finite element method are given. The next section deals with the finite volume method. Section 4 is devoted to an alternative way to obtain an $\mathcal{O}\left({h}^{2}\right)$ error bound for the finite volume method presented before. In Section 5, the technique of Section 4 is applied to derive error bounds in ${H}^{1}$ and ${L}^{\infty}$ norms. In Section 6 a lumped mass finite volume method is considered. In this case, the method loses the property of being locally conservative. Finally, the authors show that the proposed approach also applies to fully discrete schemes.

Reviewer: Ruxandra Stavre (Bucureşti)