Least-squares finite element schemes in the time domain

✍ Scribed by Krishna M. Singh; Manjeet S. Kalra

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 301 KB
• Volume: 190
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(99)00417-x

✦ Synopsis

Least-squares ®nite element procedure is used to generate recurrence relations for numerical solution of system of ordinary differential equations of the ®rst order. One-step least-squares method due to O.C. Zienkiewicz and R.W. Lewis [Earthquake Engrg. Struct. Dyn. 1 (1973) 407±408] is reviewed. An analysis of stability and other numerical properties of this method is presented, and it is found to be A-stable and second-order accurate. Using quadratic time element with Lagrange interpolation functions, a two-step leastsquares method is derived. Analysis of local discretization error, stability and other properties of the two-step method is presented. It is found that the two-step least-squares algorithm is third-order accurate and Aa-stable (a % 85 ). Comparison of numerical results obtained with the least-squares schemes with those obtained with other well known algorithms shows that the two-step least-squares scheme and three-step backward-difference scheme exhibit almost the same accuracy, whereas the one-step least-squares scheme is more accurate than one-step h-methods and two-step backward-difference scheme. Further, the least-squares schemes exhibit superior accuracy at large time values for the problems tending towards a steady state.