Error analysis of mixed finite element methods for nonlinear parabolic equations
Provides a theoretical tool (discrete embedding inequality) for error analysis of mixed finite element methods for nonlinear parabolic equations, which is a technical contribution for numerical analysts.
The authors prove a discrete embedding inequality for Raviart-Thomas mixed finite element methods and use it to derive optimal error estimates for linearized mixed finite element methods for nonlinear parabolic equations, confirmed by numerical examples.
In this paper, we prove a discrete embedding inequality for the Raviart--Thomas mixed finite element methods for second order elliptic equations, which is analogous to the Sobolev embedding inequality in the continuous setting. Then, by using the proved discrete embedding inequality, we provide an optimal error estimate for linearized mixed finite element methods for nonlinear parabolic equations. Several numerical examples are provided to confirm the theoretical analysis.