Error analysis of mixed finite element methods for nonlinear parabolic equations

2017/07/10 by Huadong Gao, Weifeng Qiu, Gao, Huadong +1
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1707.02677

openalex publication_date 2017/07/10 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Fully discrete finite element approximation for a family of degenerate parabolic mixed equations
• Optimal error estimates of mixed FEMs for second order hyperbolic\n integro-differential equations with minimal smoothness on initial data
• Unconditionally optimal error analysis of fully discrete Galerkin methods for general nonlinear parabolic equations
• Error analysis of nonconforming and mixed FEMs for second-order linear non-selfadjoint and indefinite elliptic problems
• Error estimate for a finite element approximation of the solution of a linear parabolic equation on a two-dimensional surface