THE GALERKIN FINITE ELEMENT METHOD FOR ADVECTION DIFFUSION EQUATION

ZORŞAHİN GÖRGÜLÜ M., IRK D.

SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, cilt.37, sa.1, ss.119-128, 2019 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 1
  • Basım Tarihi: 2019
  • Dergi Adı: SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Academic Search Premier, Directory of Open Access Journals
  • Sayfa Sayıları: ss.119-128
  • Anahtar Kelimeler: Cubic B-spline, Galerkin method, fourth order single step method, Crank Nicolson method, advection-diffusion equation, NUMERICAL-SOLUTION
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

Cubic B-spline Galerkin method, based on second and fourth order single step methods for time integration is used to solve numerically the advection diffusion equation (ADE). Second order single step method is also known as Crank Nicolson method. Two numerical examples are used to validate the proposed method which is found to be accurate and efficient. The effects of the advection and diffusion terms on the solution domain and the absolute error of the numerical solution are studied with the help of graphs. The obtained results show that the proposed fourth order single step method has a high success as a numerical technique for solving the ADE.