Adaptive finite element methods for diffusion and convection problems. (English) Zbl 0717.76078

Johnson, Claes

Comput. Methods Appl. Mech. Eng. 82, No. 1-3, 301-322 (1990).

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

Keywords:

adaptive h-methods; linear partial differential equations of elliptic, parabolic and hyperbolic; a posteriori error estimates; a priori error estimates

Citations:

Zbl 0644.65080

References:

[1]	Eriksson, K., Adaptive finite element methods based on optimal error estimates for linear elliptic problems, (Technical report (1987), Department of Mathematics, Chalmers University of Technology)
[2]	Eriksson, K., Adaptive finite element methods for parabolic problems II: A priori error estimates in \(L_∞(L_2)\) and \(L_∞(L_∞)\), (Technical report (1988), Department of Mathematics, Chalmers University of Technology)
[3]	Eriksson, K., Error estimates for the \(H_0^1(Σ)\) and \(L_2(Σ)\) projections onto finite element spaces under weak mesh regularity assumptions (1988), Department of Mathematics, Chalmers University of Technology
[4]	Eriksson, K.; Johnson, C., An adaptive finite element method for linear elliptic problems, Math. Comp., 50, 361-383 (1988) · Zbl 0644.65080
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