Finite element method

The finite element method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for partial differential equations. It is also referred to as finite element analysis (FEA). FEM subdivides a large problem into smaller, simpler, parts, called finite elements. The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function.

Basic concepts

The subdivision of a whole domain into simpler parts has several advantages:

A typical work out of the method involves (1) dividing the domain of the problem into a collection of subdomains, with each subdomain represented by a set of element equations to the original problem, followed by (2) systematically recombining all sets of element equations into a global system of equations for the final calculation. The global system of equations has known solution techniques, and can be calculated from the initial values of the original problem to obtain a numerical answer.

Finite

Finite is the opposite of infinite. It may refer to:

See also

Element

Element or elements may refer to:

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Cambridge

Cambridge (/ˈkeɪmbrɪdʒ/KAYM-brij) is a university city and the county town of Cambridgeshire, England, on the River Cam about 50 miles (80 km) north of London. At the United Kingdom Census 2011, its population was 123,867, including 24,488 students.

There is archaeological evidence of settlement in the area in the Bronze Age and in Roman Britain; under Viking rule, Cambridge became an important trading centre. The first town charters were granted in the 12th century, although city status was not conferred until 1951.

Cambridge is the home of the University of Cambridge, founded in 1209 and one of the top five universities in the world. The university includes the Cavendish Laboratory, King's College Chapel, and the Cambridge University Library. The Cambridge skyline is dominated by the last two buildings, along with the spire of the Our Lady and the English Martyrs Church, the chimney of Addenbrooke's Hospital and St John's College Chapel tower.

Cambridge is at the heart of the high-technology Silicon Fen with industries such as software and bioscience and many start-up companies spun out of the university. Over 40% of the workforce have a higher education qualification, more than twice the national average. Cambridge is also home to the Cambridge Biomedical Campus, one of the largest biomedical research clusters in the world, soon to be home to AstraZeneca, a hotel and relocated Papworth Hospital.