2024, Vol. 5, Issue 1, Part B
Numerical solutions for biharmonic problem via P1, P2 and P3 polynomials in both square and circular domains
Author(s): Ali Kamil Al-Abadi
Abstract: In this paper, we present a finite element method (FEM) based on the primal mixed formulation of linear and quadratic polynomials to solve the biharmonic problem in square and circular domains. We accomplish this by removing the compute-free auxiliary variable and providing a second mesh with a suitable approximation of the restriction. Consequently, a system of linear equations governs the discrete problem, which classical algorithms can solve. These equations have symmetric, positive-definite coefficients. We efficiently construct the stiffness matrix using Courant triangles. Numerical experimentation yields optimal error estimators for L2 and H1 norms. We used MATLAB R2018b software to validate the solution and create a graphical representation.
Pages: 163-173 | Views: 296 | Downloads: 98
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How to cite this article:
Ali Kamil Al-Abadi. Numerical solutions for biharmonic problem via P1, P2 and P3 polynomials in both square and circular domains. Journal of Mathematical Problems, Equations and Statistics. 2024; 5(1): 163-173.
