Numerical Integration in the DGFEM for 3D Nonlinear Convection–Diffusion Problems on Nonconforming Meshes

Abstract

The effect of numerical integration in a discontinuous Galerkin finite element method for a nonstationary nonlinear convection–diffusion problem in 3D is studied. In the space semidiscretization, the volume and surface integrals are evaluated with the aid of numerical quadratures. An estimate of the error caused by the numerical integration is presented, and it is shown what quadrature formulas guarantee preservation of the accuracy of the method with exact integration.

Keywords:

• Discontinuous Galerkin finite element method
• Error estimates
• Nonlinear convection–diffusion equation
• Numerical integration
• Truncation error

AMS Subject Classification:

• 65M60
• 65M15
• 65M12

ACKNOWLEDGMENTS

The research was a part of the research project MSM 6840770010 financed by the Ministry of Education of the Czech Republic.