The box method and some error estimation. (English) Zbl 1201.65194

Mlýnek, Jaroslav

Chleboun, J. (ed.) et al., Programs and algorithms of numerical mathematics 14. Proceedings of the seminar, Dolní Maxov, Czech Republic, June 1–6, 2008. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-55-4). 150-156 (2008).

Summary: This article focuses its attention on practical use of the box method for solving certain type of partial differential equations. The heat conduction problem of the oil transformer under stationary load is described by this equation. The knowledge of the transformer operating temperature is important for ensuring correct functionality and lifespan of transformer. We consider an elliptic partial differential equation of second order with the Newton boundary condition on a rectangular domain. The paper contains description of a numerical solution procedure of the heat problem and an estimation of local discretization error. The box method is often called the finite volume method, too. The solution of practical examples are presented as well.
For the entire collection see [Zbl 1194.65013].

MSC:

65N08	Finite volume methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations
65M08	Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
35K05	Heat equation

Keywords:

numerical examples; box method; heat conduction problem; elliptic equation; local discretization error; finite volume method