Blended infinite elements for paraboblic boundary value problems

✍ Scribed by James C. Cavendish; Charles A. Hall; O. C. Zienkiewicz

• Publisher: John Wiley and Sons
• Year: 1978
• Tongue: English
• Weight: 524 KB
• Volume: 12
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620121206

✦ Synopsis

A common method for numerically approximating two-point parabolic boundary value problems of the form u, = L[u] +f(u) defined on the semi-infinite strip S = [0, 11 X [0, 00) is to first discretize the spatial operator in the differential equation and then solve for the time evolution. Such an approach typically involves solving a system of algebraic equations at a sequence of time steps. In this paper we take a different approach and subdivide S into a collection of semi-infinite substrips S, = [x,, x,,,] x [0, a), and use blending function techniques to derive finite parameter functions e,(x, I ) defined on S,. Spectral matching methods are used in deriving e, to ensure that (u -e , ) can be made small on S,. Galerkin's method, with associated integrations over the entire space-time domain S, is then used to generate approximations to u ( x , t ) based upon the so defined infinite elements (e,, S,). Approximations are hence found for all (x, 1 ) in S by solving one well structured system of algebraic equations. We apply the method to several linear and non-linear problems.