Error estimation for nonlinear elliptic problems using the $h$-$p$-mixed finite element method in $3$ dimensional space
Bull. Korean Math. Soc. 2001 Vol. 38, No. 2, 237-260
Miyoung Lee
Kangnam University
Abstract : The approximation properties for $L^2$-projection, Raviart-Thomas projection, and inverse inequality have been derived in $3$ dimensional space. $h$-$p$-mixed finite element methods for strongly nonlinear second order elliptic problems are proposed and analyzed in $3D$. Solvability and convergence of the linearized problem have been shown through duality argument and fixed point argument. The analysis is carried out in detail using Raviart-Thomas-Nedelec spaces as an example.
Keywords : nonlinear elliptic problem, mixed method
MSC numbers : 65N22, 65N12, 35J25, 35J60, 74S05, 74S25
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