Adaptive Finite Element Method for Solving Poisson Partial Differential Equation

Authors

  • Gokul KC Kathmandu University, Dhulikhel, Nepal
  • Ram Prasad Dulal Kathmandu University, Dhulikhel, Nepal

DOI:

https://doi.org/10.3126/jnms.v4i1.37107

Keywords:

Poisson equation, Finite element method, Posteriori error analysis, Adaptive mesh refinement

Abstract

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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Author Biographies

Gokul KC, Kathmandu University, Dhulikhel, Nepal

Department of Mathematics, School of Science

Ram Prasad Dulal, Kathmandu University, Dhulikhel, Nepal

Department of Mathematics, School of Science

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Published

2021-05-14

How to Cite

KC, G., & Dulal, R. P. (2021). Adaptive Finite Element Method for Solving Poisson Partial Differential Equation. Journal of Nepal Mathematical Society, 4(1), 1–18. https://doi.org/10.3126/jnms.v4i1.37107

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Section

Articles