Fundamentals of finite element method

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Department of Technical Mathematics

Synopsis:

Variational formulation of boundary value problems for partial differential equations, weak solution, matematical fundaments of finite element method (FEM). Relation between weak and classical solution. Error estimates. FEM for eliptic, parabolic and hyperbolic equations. Examples in 1D, 2D. Applications of finite element method: heat equation, wave equation, convection-diffusion equation, linear elasticity problem, Stokes problem and Navier-Stokes equations.

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Study materials:

Johnson, C.: Numerical Solution of Partial Differential Equation by the Finite Element Method, 1987, Cambridge University Press.

Míka, S., Přikryl, P.: Numerické metody řešení parciálních diferenciálních rovnic, 1995, ZČU Plzeň.

Sváček, P., Feistauer, M.: Metoda konečných prvků, 2006, Vydavatelství ČVUT.

Vitásek, E.: Numerické metody, 1987, SNTL.

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