𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Verified computation of solutions for obstacle problems with guaranteed L∞ error bound

✍ Scribed by C.S. Ryoo

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
327 KB
Volume
14
Category
Article
ISSN
0893-9659

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we consider a numerical enclosure method with guaranteed Loo error bound for the solutions of obstacle problems. Using the finite-element approximations and the explicit a priori error estimates for obstacle problems, we present an effective verification procedure that automatically generates on a computer a set which includes the exact solution. A particular emphasis is that our method needs no assumption of the existence of the solution of the original obstacle problems, but it follows as the result of computation itself. A numerical example for an obstacle problem is presented.

📜 SIMILAR VOLUMES

Guaranteed computable bounds for the exa
Guaranteed computable bounds for the exact error in the finite element solution—Part II: bounds for the energy norm of the error in two dimensions
✍ T. Strouboulis; I. Babuška; S. K. Gangaraj 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 551 KB

This paper addresses the computation of guaranteed upper and lower bounds for the energy norm of the exact error in the ÿnite element solution. These bounds are constructed in terms of the solutions of local residual problems with equilibrated residual loads and are rather sharp, even for coarse mes

Correction to “mixed problems for the ti
Correction to “mixed problems for the time-dependent telegraph equation: Continuous numerical solutions with a priori error bounds”: Mathl. comput. modelling vol. 25, no. 11, pp. 31–44, 1997
✍ L. Jödar; D. Goberna 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 248 KB

This paper deals with the correction of Section 2 of (11 that is incorrect starting from formula (2.5). The correction is based on the replacement of hypotheses (1.6) and (1.7) by new conditions. Minor consequences is Sections 3 and 4 of [l] are also rectified.