A Fully-Discrete Finite Element Approximation for the Eddy Currents Problem

Ingeniería y Ciencia

Acevedo, Ramiro¹  Loaiza, Gerardo¹ 

[1] Universidad del Cauca, Popayán, Colombia

关键词: Transient eddy current model;    potential formulation;    fully-discrete approximation;    finite elements;    error estimates;   

DOI  :  

学科分类：工程和技术（综合）

来源: Universidad E A F I T

【 摘 要 】

The eddy current model is obtained from Maxwell's equations by neglecting the displacement currents in the Ampère-Maxwell's law. The so-called ''A, V - A potential formulation'' is nowadays one of the most accepted formulations to solve the eddy current equations numerically, and Bíró & Valli have recently provided its well-posedness and convergence analysis for the time-harmonic eddy current problem. The aim of this paper is to extend the analysis performed by Bíró & Valli to the general transient eddy current model. We provide a backward-Euler fully-discrete approximation based on nodal finite elements and we show that the resulting discrete variational problem is well posed. Furthermore, error estimates that prove optimal convergence are settled.

【 授权许可】

Unknown