RUcore feed creatorurn:uuid:6214fd4d-7c6d-a553-5dc0-447e268b1c49RUcore Syndication System, v1.0Copyright 2020, Rutgers, The State University of New JerseyA frequency analysis of finite difference and finite element methods for initial value problemshttps://doi.org/doi:10.7282/t3-t7nc-c009Vichnevetsky, RobertDe Schutter, F.1975-07-01T00:00:00-04:00The popularity of finite element and spline methods has brought to the fore the need for criteria to compare the accuracy of computing algorithms. Several recent papers have addressed this problem, investigating the use of new analytical tools to achieve this goal (see e.g. Swartz and jWendroff (1974 a and b) Vichnevetsky (1973), Vichnevetsky, Tu and Steen (1974) Fix and Strang (1969)).
The approach used here consists in considering simple partial differential equations as typical models of more complex ones, and in showing that the error introduced by numerial approximations may be characterized, for those simple models by criteria which can be related to physical parameters of those equations. The mathematics are based onn the expression of solutions as a sum of space-sinusoidal components for which errors can be expressed as a function of the frequency.