The Error Analysis two-dimension nonlinear convection diffusion problem by using Crank- Nicolson Petrov Weak Galerkin

Abstract

In this paper, focuses on the formulation and investigation of two dimensional non-linear Convection diffusion equations using the Crank–Nicolson Petrov weak Galerkin finite element approach. We apply weak Galerkin finite element method and Petrov Galerkin finite element mothed. we defining a space of the Petrov Weak Galerkin finite element method that depends on a test function space differs from the trial function space the value a constant stability parameter of the delta parameter. The stability and error estimate full-discrete is proved and the approximate solutions are convergent with the error of .  The analysis addresses stability properties, derives error estimates, and establishes optimal convergence rates in both the and norms for the Petrov weak Galerkin finite element PWGFE scheme. In addition, the numerical results of PWGFE method show the convergence and accuracy of the method. several numerical experiments are conducted to validate the theoretical findings.

DOI: https://doi.org/10.54633/2333-025-059-022