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A symmetric finite volume scheme for selfadjoint elliptic problems. (English) Zbl 1027.65150
The authors introduce a new symmetric finite volume scheme for a general self-adjoint elliptic boundary value problem. Some relations between finite volume methods and finite difference methods are discussed. Some error estimates are provided for the \(L^2\)-norm, \(H^1\)-norm and \(L^{\infty}\)-norm. Furthermore, post-processing techniques are presented. Finally, some numerical results are performed on two academic cases.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N15 Error bounds for boundary value problems involving PDEs
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