Name
Abstract | ||
|---|---|---|
This paper deals with the numerical solution of an axisymmetric transient eddy current problem in a conductive non-linear magnetic media. This means that the relation between the magnetic field and the magnetic induction (i.e., the so-called B - H curve) is non-linear. We analyze a weak formulation of the resulting problem in the axisymmetric case, with the source term given by means of a non-homogeneous Dirichlet boundary condition. For its numerical approximation, we propose a fully discrete scheme based on a finite element method combined with a backward Euler time discretization. We establish its well-posedness and derive error estimates in appropriate norms for the proposed scheme. In particular, we obtain an L 2 rate of convergence of order O ( h + Δ t ) without assuming any additional regularity of the solution. Moreover, under appropriate smoothness assumptions, we also prove an L 2 -like rate of convergence of order O ( h 2 + Δ t ) . Finally, some numerical results, which confirm the theoretically predicted behavior of the method, are reported. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1016/j.camwa.2015.08.017 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
Transient eddy current,Axisymmetric problem,Non-linear partial differential equations,Non-homogeneous Dirichlet boundary condition,Finite elements | Discretization,Mathematical optimization,Mathematical analysis,Dirichlet boundary condition,Finite element method,Rate of convergence,Eddy current,Numerical analysis,Backward Euler method,Mathematics,Weak formulation | Journal |
Volume | Issue | ISSN |
70 | 8 | 0898-1221 |
Citations | PageRank | References |
1 | 0.39 | 7 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alfredo Bermúdez | 1 | 47 | 13.97 |
| Dolores Gómez Pedreira | 2 | 5 | 1.97 |
| R. Rodríguez | 3 | 72 | 19.18 |
| Pablo Venegas | 4 | 1 | 0.39 |