Publication

A finite element method for 3D hydrostatic water flows

Alfio Quarteroni
1999
Conference Papers

Abstract

We propose a numerical method for the solution of the Quasi3D hydrodynamic equations. This approach uses a combination of standard linear finite elements along the vertical direction and non-conforming Raviart-Thomas elements in the horizontal planes. We describe, also, a suitable approximation for the convective terms

Official source

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Alfio Quarteroni
1999
Conference Papers

Abstract

Official source

Related concepts (26)

Finite element method

The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

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A finite element method for 3D hydrostatic water flows

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