The finite element method for a degenerate hyperbolic partial differential equation

1983 ◽  
Vol 23 (2) ◽  
pp. 231-238
Author(s):  
William J. Layton
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Partial Differential Equation ◽  
Finite Element ◽  
Hyperbolic Partial Differential Equation ◽  
The Finite Element Method ◽  
Partial Differential ◽  
Element Method

Adaptive Finite Element Method for Solving Poisson Partial Differential Equation

2021 ◽  
Vol 4 (1) ◽  
pp. 1-18
Author(s):  
Gokul KC ◽  
Ram Prasad Dulal
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Partial Differential Equation ◽  
Finite Element ◽  
Poisson Equation ◽  
Rectangular Domain ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Partial Differential ◽  
Element Method

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.

scholarly journals Design of a nonlinear observer using the finite element method with application to a biological system

2019 ◽  
pp. 292-297 ◽  
Author(s):  
Branislav Rehak ◽  
Volodymyr Lynnyk
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Partial Differential Equation ◽  
Finite Element ◽  
Biological System ◽  
Specific Growth ◽  
Observer Design ◽  
Nonlinear Observer ◽  
The Finite Element Method ◽  
Element Method

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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