Abstract
A discontinuous finite-element method is presented for solving the linear advection-diffusion equation, based on the Residual-Free Bubble (RFB) finite-element formulation. After the macro-scales (usual piecewise-polynomials elements) are separated from the micro-scales (the bubble part), they are computed by a standard Galerkin formulation, while the bubble part is approximated by a discontinuous Galerkin method. The advantage of this approach, as compared to other implementations of the Residual-Free Bubble formulation, is that the macro-scales are computed accurately, at least for the model problem presently considered. Numerical tests are performed to confirm the validity of the proposed approach.
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Sangalli, G. A discontinuous residual-free bubble method for advection-diffusion problems. Journal of Engineering Mathematics 49, 149–162 (2004). https://doi.org/10.1023/B:ENGI.0000017479.62697.66
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DOI: https://doi.org/10.1023/B:ENGI.0000017479.62697.66