• Madan Nagre

In this paper, I have presented a new approach for solving general 2D partial differential equations using the finite element method with the help of isoparametric quadrilateral element for mapping arbitrary shape domains. The concept behind this approach is to partition the whole geometrical domain into the minimum quadrilateral elements. This approach focuses on using isoparametric elements (minimum) to cover the whole complex domain. This is achieved by partitioning the whole domain into 1 to 4 isoparametric elements (irregular, curved edge type elements) then it is mapped into regular rectangular elements in the natural coordinate system using the Lagrangian interpolation basis function and Jacobin matrix. After this, the method of residual and Galerkin method is used to solve the weak form of the governing differential equation.

finite element method, fem, isoparametric formulation, Jacobian transformation, minimum element domain partition, Galerkin method, Laplace equation.

"GENERALIZED FINITE ELEMENT METHOD-ISOPARAMETRIC DOMAIN TRANSFORMATION (MINIMUM ELEMENTS APPROACH)", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.9, Issue 5, page no.i258-i267, May-2022, Available :http://www.jetir.org/papers/JETIR2205937.pdf

"GENERALIZED FINITE ELEMENT METHOD-ISOPARAMETRIC DOMAIN TRANSFORMATION (MINIMUM ELEMENTS APPROACH)", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.9, Issue 5, page no. ppi258-i267, May-2022, Available at : http://www.jetir.org/papers/JETIR2205937.pdf