Alessandro Russo

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We propose a family of mimetic discretization schemes for elliptic problems including convection and reaction terms. Our approach is an extension of the mimetic methodology for purely diffusive problems on unstructured polygonal and polyhedral meshes. The a priori error analysis relies on the connection between the mimetic formulation and the lowest order(More)
Residual-free bubbles have been recently introduced in order to compute optimal values for the stabilization methods a la Hughes-Franca. However, unless in very special situations, (one-dimensional problems, limit cases, etc.) they require the actual solution of PDE problems (the bubble problems) in each element. Thus they are very diicult to be used in(More)
We further consider the Galerkin method for advective-diiusive equations in two-dimensions. The nite dimensional space employed is of piecewise polynomials enriched with residual-free bubbles (RFB). We show that, in general, this method does not coincide with the SUPG method, unless the piecewise polynomials are spanned by linear functions. Furthermore a(More)
We develop an a priori error analysis of a nite element approximation to the elliptic advection-diiusion equation ?"u + a ru = f subject to a homogeneous Dirichlet boundary condition, based on the use of residual-free bubble functions. An optimal order error bound is derived in the so-called stability-norm "krvk 2 L 2 (() + X T h T ka rvk 2 L 2 (T) ! 1=2 ;(More)
We present an overview of stabilized nite element methods and of the standard Galerkin method enriched with residual-free bubble functions. The inadequacy of the standard Galerkin method using piecewise polyno-mials is discussed for diierent applications; the treatment using stabilized methods in their diierent versions is reviewed; and the connection to(More)