Penyelesaian Numerik Persamaan Burgers Menggunakan Metode Elemen Hingga

Astuti, Laila Tri and Nur Shofianah, S.Si., M.Si., Ph.D. (2024) Penyelesaian Numerik Persamaan Burgers Menggunakan Metode Elemen Hingga. Sarjana thesis, Universitas Brawijaya.

Abstract

Pada skripsi ini dibahas penyelesaian numerik persamaan Burgers satu dimensi. Persamaan Burgers satu dimensi merupakan persamaan diferensial parsial yang bergantung pada domain spasial dan waktu. Domain spasial didiskretisasi menggunakan metode elemen hingga, sedangkan domain waktu didekati menggunakan aturan trapesium. Pendekatan domain waktu menggunakan aturan trapesium menghasilkan skema yang mirip dengan skema Crank-Nicolson. Kelebihan metode elemen hingga yaitu dapat menyesuaikan domain yang tidak beraturan dan dapat menyelesaikan masalah kondisi batas yang kompleks. Orde akurasi untuk penyelesaian numerik persamaan Burgers menggunakan metode elemen hingga masih belum dapat ditentukan karena terjadi peningkatan error pada saat ∆t diperkecil.

English Abstract

In this final project, we discuss the numerical solution of the onedimensional Burgers equation. The one-dimensional Burgers equation is a partial differential equation that depends on the spatial and time domains. The spatial domain is discretized using the finite element method, while the time domain is approached using the trapezoidal rule. Approaching the time domain using the trapezoidal rule results in a scheme similar to the Crank-Nicolson scheme. The advantages of the finite element method are that it can fit irregular domains and can solve complex boundary condition problems. The order of accuracy for the numerical solution of the Burgers equation using the finite element method is still undetermined because there is an increase in error when ∆t is minimized.In this final project, we discuss the numerical solution of the onedimensional Burgers equation. The one-dimensional Burgers equation is a partial differential equation that depends on the spatial and time domains. The spatial domain is discretized using the finite element method, while the time domain is approached using the trapezoidal rule. Approaching the time domain using the trapezoidal rule results in a scheme similar to the Crank-Nicolson scheme. The advantages of the finite element method are that it can fit irregular domains and can solve complex boundary condition problems. The order of accuracy for the numerical solution of the Burgers equation using the finite element method is still undetermined because there is an increase in error when ∆t is minimized.

Text (DALAM MASA EMBARGO) Laila Tri Astuti.pdf Restricted to Registered users only Download (2MB)

Actions (login required)

View Item