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Adaptive streamline diffusion finite element methods for stationary convection-diffusion problems. (English) Zbl 0795.65074
Summary: Adaptive finite element methods for stationary convection-diffusion problems are designed and analyzed. The underlying discretization scheme is the shock-capturing streamline diffusion method. The adaptive algorithms proposed are based on a posteriori error estimates for this method leading to reliable methods in the sense that the desired error control is guaranteed. A priori error estimates are used to show that the algorithms are efficient in a certain sense.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65Y20 Complexity and performance of numerical algorithms
35K20 Initial-boundary value problems for second-order parabolic equations
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