Finite element method for Grwünwald–Letnikov time-fractional partial differential equation

2013 ◽  
Vol 92 (10) ◽  
pp. 2103-2114 ◽  
Author(s):  
Xindong Zhang ◽  
Juan Liu ◽  
Leilei Wei ◽  
Changxiu Ma
2021 ◽  
Vol 4 (1) ◽  
pp. 1-18
Author(s):  
Gokul KC ◽  
Ram Prasad Dulal

Poisson equation is an elliptic partial differential equation, a generalization of Laplace equation. Finite element method is a widely used method for numerically solving partial differential equations. Adaptive finite element method distributes more mesh nodes around the area where singularity of the solution happens. In this paper, Poisson equation is solved using finite element method in a rectangular domain with Dirichlet and Neumann boundary conditions. Posteriori error analysis is used to mark the refinement area of the mesh. Dorfler adaptive algorithm is used to refine the marked mesh. The obtained results are compared with exact solutions and displayed graphically.


2019 ◽  
pp. 292-297 ◽  
Author(s):  
Branislav Rehak ◽  
Volodymyr Lynnyk

An observer for a nonlinear biological system — biomass production in a bioreactor —is proposed. The specific growth rate is estimated. The key point of the observer design is finding a solution of a certain partial differential equation. Conditions guaranteeing existence of its solution are presented. The solution is approximated using finite element method. The results are illustrated by a numerical example.


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