A COMBINED CONTINUOUS-DISCONTINUOUS FINITE ELEMENT METHOD FOR CONVECTION-DIFFUSION PROBLEMS

Abstract

DISCONTINUOUS GALERKIN (DGM) METHOD COMBINES THE ADVANTAGES OF STABILITY OF FINITE VOLUME METHOD AND THE ACCURACY OF CONTINUOUS FINITE ELEMENT METHOD (FEM). APPLICATIONS OF THE DGM ARE PARTICULARLY VALUABLE WHERE THE SOLUTION PRESENTS HIGH-GRADIENTS OR DISCONTINUITIES, SUCH AS BOUNDARY LAYERS AND SHOCK PROBLEMS. A DISADVANTAGE OF THE DGM IS THE HIGHER COMPUTATIONAL COST WHEN COMPARING TO CLASSIC FINITE ELEMENT METHOD, DUE TO THE NCREASED NUMBER OF DEGREES OF FREEDOM. WITH THIS MOTIVATION, IN THIS PAPER WE EXPLORE THE IDEA OF COMBINING CONTINUOUS AND DISCONTINUOUS GALERKIN FORMULATIONS FOR THE SIMULATION OF CONVECTION-DIFFUSION PROBLEMS. THE COMPUTATIONAL DOMAIN IS DECOMPOSED INTO TWO PARTS. IN ONE REGION THE SOLUTION IS SUPPOSED TO BE SMOOTH, AND THE TRADITIONAL CONTINUOUS FINITE ELEMENT METHOD IS APPLIED. ON THE OTHER HAND, WHERE STEEP GRADIENTS ARE EXPECTED, WE USE A DISCONTINUOUS GALERKIN FORMULATION. THIS PAPER PRESENTS NUMERICAL RESULTS FOR THE COMBINED FEM/DGM METHOD APPLIED TO CONVECTION-DIFFUSION PROBLEMS.