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Adaptive finite element methods for diffusion and convection problems. (English) Zbl 0717.76078
Summary: We give a survey of recent results obtained together with K. Eriksson on adaptive h-methods for the basic linear partial differential equations of elliptic, parabolic and hyperbolic type [e.g., Math. Comput. 50, No.182, 361-383 (1988; Zbl 0644.65080)]. Our adaptive algorithms are based on a posteriori error estimates leading to reliable methods, and comparison with sharp a priori error estimates is made to prove efficiency of the procedures.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76R50 Diffusion
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