# zbMATH — the first resource for mathematics

The finite volume element method for diffusion equations on general triangulations. (English) Zbl 0729.65086
The authors prove the convergence and get a priori error estimates for the approximation of diffusion equations of the form $$-\nabla (A\nabla u)=f$$ in $$\Omega$$, $$u=0$$ on $$\partial \Omega$$ by the finite volume element method. The two dimensional domain $$\Omega$$ is assumed to be polygonal and exactly covered by a general Delaunay-Voronoi triangulation with no interior angle larger than 90$$\circ$$. Thus they prove O(h) estimates of the error in a discrete $$H^ 1$$-seminorm and a $$O(h^ 2)$$ estimate under an additional assumption concerning local uniformity of the triangulation.

##### MSC:
 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 76R50 Diffusion 35J25 Boundary value problems for second-order elliptic equations
Full Text: