The Residual–Free Bubble Method for Problems with Multiple Scales Andrea Cangiani St Hugh’s College Doctor of Philosophy Trinity Term 2004 This thesis is devoted to the numerical analysis and development of the residual–free bubble finite element method. We begin with an overview of known results and properties of the method, showing how techniques used on a range of multiscale problems can be ...

Gene network dynamics often involves processes that take place on widely differing time scales – from the order of nanoseconds to the order of several days. Multiple time scales in mathematical models often lead to serious computational difficulties, such as numerical stiffness in the case of differential equations or excessively redundant Monte Carlo simulations in the case of stochastic proce...

An alternative example of the method of multiple scales is presented. This example arises in the study of the classical heat equation with a slowly varying flux imposed at one end. The module presents introductory ideas about dimensionless variables, multiple-scale expansions, and scaling of the dependent variable. The necessarily obfuscating algebraic computation is less than that for more fam...