A finite element method for Maxwell polynomial chaos Debye model

摘要

‘In this paper, a finite element method is presented to approximate Maxwell–Polynomial Chaos(PC) Debye model in two spatial dimensions. The existence and uniqueness of the weak solutions are presented firstly according with the differential equations by using the Laplace transform. Then the property of energy decay with respect to the time is derived. Next, the lowest Nédélec–Raviart–Thomas element is chosen in spatial discrete scheme and the Crank–Nicolson scheme is employed in time discrete scheme. The stability of full-discrete scheme is explored before an error estimate of accuracy O(Δt2+h) is proved under the L2−norm. Numerical experiment is demonstrated for showing the correctness of the results.