Symmetric modified finite volume element methods for selfadjoint elliptic and parabolic problems (Q1860386)

The author introduces a symmetric finite volume element method for selfadjoint elliptic and parabolic partial differential equations. The symmetry of the resulting linear system, which in usual approaches is non-symmetric, is obtained by adding a high-order term to the original system. Proofs of optimal order energy norm error estimates are given and it is shown that the difference between the symmetric and non-symmetric solutions is a high order term.