Analysis of optimal finite-element meshes in R

Journal Article · Sun Apr 01 04:00:00 EST 1979 · Math. Comput.; (United States)

DOI:https://doi.org/10.2307/2006290· OSTI ID:6244980

Babuska, I; Rheinboldt, W C

A theory of a posteriori estimates for the finite-element method was developed earlier by the authors. Based on this theory, for a two-point boundary value problem the existence of a unique optimal mesh distribution is proved and its properties analyzed. This mesh is characterized in terms of certain, easily computable local error indicators which in turn allow for a simple adaptive construction of the mesh and also permit the computation of a very effective a posteriori error bound. While the error estimates are asymptotic in nature, numerical experiments show the results to be excellent already for 10% accuracy. The approaches are not restricted to the model problem considered here only for clarity; in fact, they allow for rather straightforward extensions to more general problems in one dimension, as well as to higher-order elements.

• OSTI ID: 6244980
• Journal Information: Math. Comput.; (United States), Journal Name: Math. Comput.; (United States) Vol. 33:146; ISSN MCMPA
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ASYMPTOTIC SOLUTIONS
BOUNDARY-VALUE PROBLEMS
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE ELEMENT METHOD
NUMERICAL SOLUTION
OPTIMIZATION