A Discontinuous Finite-Element Formulation of the Gray Radiative Heat Transfer P1 Equations Using a Moving Mesh Partial Differential Equation

2019 ◽  
Author(s):  
L. Chacón ◽  
H. Hammer ◽  
H. Park ◽  
W. Taitano
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Element ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Moving Mesh ◽  
Element Formulation ◽  
Partial Differential ◽  
Discontinuous Finite Element

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.

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