An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems

We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm, under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems.

A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems

We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. The performance of the proposed estimators within an automatic hp-adaptive refinement procedure is studied through numerical experiments.

Review of order fulfilment models for Catalogue Mass Customization

Mass Customization (MC) is not a mature business strategy and hence it is not clear that a single or small group of operational models are dominating. Companies tend to approach MC from either a mass production or a customization origin and this in itself gives reason to believe that several operational models will be observable. This paper reviews actual and theoretical fulfilment systems that enterprises could apply when offering a pre-engineered catalogue of customizable products and options. Issues considered are: How product flows are structured in relation to processes, inventories and decoupling point(s); - Characteristics of the OF process that inhibit or facilitate fulfilment; - The logic of how products are allocated to customers; - Customer factors that influence OF process design and operation. Diversity in the order fulfilment structures is expected and is found in the literature. The review has identified four structural forms that have been used in a Catalogue MC context: - fulfilment from stock; - fulfilment from a single fixed decoupling point; - fulfilment from one of several fixed decoupling points; - fulfilment from several locations, with floating decoupling points. From the review it is apparent that producers are being imaginative in coping with the demands of high variety, high volume, customization and short lead times. These demands have encouraged the relationship between product, process and customer to be re-examined. Not only has this strengthened interest in commonality and postponement, but, as is reported in the paper, has led to the re-engineering of the order fulfilment process to create models with multiple fixed decoupling points and the floating decoupling point system