## The Later Years

He remained at Swansea until his retirement at age 67 in 1988 and subsequently became Professor Emeritus of the University of Wales, as well as holding the UNESCO Chair of Numerical Methods in Engineering at the University of Technology of Catalunya, Barcelona for 15 years. Although formally retired, he remained active in finite element research.

The ‘holy grail’ in the field of finite elements had been a search for a method of estimating the error in the computational solution – a difficult task given that the exact solution to the problem is invariably unknown. This was of long time concern to Olek and he first turned his attention to addressing the problem in 1983, a few years before his retirement. Work in this area had been undertaken by mathematicians, largely originated by I. Babuska, since the mid 1970s, which led to Olek, in collaboration with Babuska, developing procedures for practical problems, in the context of p-refinement, through construction of an appropriate error measure (51). Further progress took place over the next few years culminating in the so-called ‘Zienkiewicz-Zhu (Z2)’, method (52, 53) that he principally developed with his Ph.D. student J. Z. Zhu. This procedure represented the single most significant advancement in the control of error in finite element analysis and is widely used to the present day. The method relies upon using the difference between the smoothed and unsmoothed finite element solutions to construct a local error measure and then employing adaptive mesh refinement to equalise this error over the entire domain. Zienkiewicz’s work on the topic continued into the 1990s with publication of an improved error estimation procedure, termed the ‘Superconvergent Patch Recovery’ which is based on the superconvergence properties of certain points within the finite elements (54). It is worth noting that Olek was over 70 years old when this work was completed, which arguably is one of his most important contributions to finite element research.

In the years leading to his formal retirement, a substantial portion of Olek’s research moved into the field of computational fluid dynamics. Commencing in 1983, with colleagues, K. Morgan, R. LÅ‘hner and J. Peraire, finite element approaches were extended to the field of high speed compressible flow, where traditionally finite difference or finite volume approaches held sway. This allowed for the first time high speed flows, including supersonic behaviour, to be solved effectively using finite elements (55, 56). In the practical problem of shock capture, the need for mesh adaptation employing automatic remeshing is paramount and the developments undertaken in error estimation and adaptive refinement mentioned above proved to be of crucial importance in this respect.

After retirement from Swansea in 1987, Olek spent two months each year at the International Centre for Numerical Methods in Engineering (CIMNE) at Universitat Politecnica de Catalunya (UPC) in Barcelona, Spain, brought about by his close connection with Eugenio Oñate. Formerly Olek’s Ph.D. student, Oñate moved to the Technical University of Catalunya (UPC) in Barcelona, where he subsequently founded the International Center for Numerical Methods in Engineering (CIMNE), a research centre specializing in the development and application of numerical methods in engineering. In 1989 Olek was appointed to the UNESCO Chair of Numerical Methods in Engineering at UPC. This was the very first UNESCO Chair in the world and arose from interactions with G. S. Holister who was working at UNESCO developing support to technology and engineering and who previously had been on the Civil Engineering staff at Swansea. The idea for such a position arose from the book “Small World” by David Lodge (1984). In the book professors of literature imagine a UNESCO Chair that will allow them to retire into a world of continuous travel with no lecturing obligations at an extravagant salary. The award to Olek attracted interest worldwide and was taken as a model to create many other UNESCO Chairs in different fields in universities around the world. Today there exist some three hundred such UNESCO Chairs.

While Olek did continue to travel extensively for many years after his retirement, he devoted much of his UNESCO Chair activities in Spain to working with colleagues at CIMNE on several topics. In the area of fluid mechanics, much of Olek’s efforts were directed at developing a ‘general fluid mechanics algorithm’. To this end, together with principally R. Codina, he developed a general algorithm for compressible and incompressible flows, termed the Split, Characteristic Based (CBS) scheme (57). He refused to distinguish between finite element and finite volume approaches, believing them to be computationally very similar, but preferred the finite element approximation in transient problems where he held the view that the correct ‘mass matrices’ generated add considerably to the accuracy viz a viz the lumped forms traditionally used by the ‘difference’ proponents.

Olek’s other great passion over the remaining period of his life was revision and extension of his finite element books.