Finite Element Solution of Poisson Equation over Polygonal Domains using an Explicit Integration Scheme and a novel Auto Mesh Generation Technique (International Journal of Engineering and Computer Science, 2016)
This paper presents an explicit finite element integration scheme to compute  the stiffness matrices for linear convex quadrilaterals. Finite element formulationals  express stiffness matrices  as double integrals of the  products of global derivatives. These  integrals  can be shown to depend on  triple products of the  geometric properties matrix and the  matrix of  integrals  containing the rational functions with polynomial numerators  and linear denominator in bivariates as  integrands over a 2-square. These  integrals are computed explicitely by using symbolic mathematics capabilities of MATLAB. The proposed explicit  finite  element integration scheme can be applied solve boundary value problems  in continuum mechanics over convex polygonal domains.We have  also developed  an automatic  all quadrilateral  mesh generation  technique for convex polygonal  domain  which provides the nodal coordinates and element connectivity. We have used  the explicit integration  scheme and the novel mesh generation technique  to solve the  Poisson equation with given Dirichlet  boundary conditions over convex  polygonal domains.