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Further considerations on residual-free bubbles for advective-diffusive equations. (English) Zbl 0934.65126
First, the authors detail the residual-free bubble method in the frames of a Galerkin approach for the numerical solution of a second-order elliptic boundary value problem. Then the method is specialized to linear or bilinear elements and the advection-diffusion equation in 2D. For the extra terms (as compared to standard Galerkin) arising from the bubbles and for vanishing diffusion, an estimate is obtained which quantifies that bubbles add stability. Further, the relation of the bubble approach to the streamline diffusion method is investigated. Finally, results of numerical experiments illustrate that there is no essential difference between the results produced by both methods.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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