This paper is concerned with the superconvergence error estimates of a classical mixed finite element method for a nonlinear parabolic/elliptic coupled thermistor equations.The method is based on a popular combination...This paper is concerned with the superconvergence error estimates of a classical mixed finite element method for a nonlinear parabolic/elliptic coupled thermistor equations.The method is based on a popular combination of the lowest-order rectangular Raviart-Thomas mixed approximation for the electric potential/field(φ,θ)and the bilinear Lagrange approximation for temperature u.In terms of the special properties of these elements above,the superclose error estimates with order O(h^(2))are obtained firstly for all three components in such a strongly coupled system.Subsequently,the global superconvergence error estimates with order O(h^(2))are derived through a simple and effective interpolation post-processing technique.As by a product,optimal error estimates are acquired for potential/field and temperature in the order of O(h)and O(h^(2)),respectively.Finally,some numerical results are provided to confirm the theoretical analysis.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12101568,12071443).
文摘This paper is concerned with the superconvergence error estimates of a classical mixed finite element method for a nonlinear parabolic/elliptic coupled thermistor equations.The method is based on a popular combination of the lowest-order rectangular Raviart-Thomas mixed approximation for the electric potential/field(φ,θ)and the bilinear Lagrange approximation for temperature u.In terms of the special properties of these elements above,the superclose error estimates with order O(h^(2))are obtained firstly for all three components in such a strongly coupled system.Subsequently,the global superconvergence error estimates with order O(h^(2))are derived through a simple and effective interpolation post-processing technique.As by a product,optimal error estimates are acquired for potential/field and temperature in the order of O(h)and O(h^(2)),respectively.Finally,some numerical results are provided to confirm the theoretical analysis.
