This work presents a study on the performance of nodal bases on triangles and on quadrilaterals for discontinuous Galerkin solutions of hyperbolic conservation laws. A nodal basis on triangles and two tensor product nodal bases on quadrilaterals are considered. The quadrilateral element bases are constructed from the Lagrange interpolating polynomials associated with the Legendre–Gauss–Lobatto ...

We consider the approximation properties of finite element spaces on quadrilateral meshes. The finite element spaces are constructed starting with a given finite dimensional space of functions on a square reference element, which is then transformed to a space of functions on each convex quadrilateral element via a bilinear isomorphism of the square onto the element. It is known that for affine...

An 8-node quadrilateral plane element US-QUAD8 is developed for linear isotropic hardening material in the framework of updated Lagrangian unsymmetric finite formulation where B L matrix constructed by classical shape function, and R higher-order basis function global coordinate system. The present eliminates influence Jacobian elemental stiffness guarantees quadratic completeness displacement ...

Certain difficulties with the use of quadrilateral or hexahedral finite elements are related to mesh refinement and to element compatibility and quality after refinement. In this paper, special refinement elements are presented that make possible connecting two special elements to one edge of an 8-node quadrilateral element (2D). The main idea in refinement elements is to place some midside nod...

We study the mixed Dirichlet–Neumann problem for Laplace equation in complement of a bounded convex polygonal quadrilateral extended complex plane. The Dirichlet / Neumann conditions at opposite pairs sides are $$\{0,1\}$$ and $$\{0,0\},$$ resp. solution to this is harmonic function unbounded polygon known as potential quadrilateral. compute values u including its value infinity. main result pa...

This paper reports numerical analyses of free vibration of laminated composite plate/ shell structures of various shapes, span-to-thickness ratios, boundary conditions and lay-up sequences. The method is based on a novel four-node quadrilateral element, namely MISQ20, within the framework of the first-order shear deformation theory (FSDT). The element is built by incorporating a strain smoothin...

A general 2D-hp-adaptive Finite Element FE implementation in Fortran 90 is described. The implementation is based on an abstract data structure, which allows to incorporate the full hp-adaptivity of triangular and quadrilateral nite elements. The h-reenement strategies are based on h2-reenement of quadrilaterals and h4-reenement of triangles. For p-reenement we allow the approximation order to ...

Schneiders and Debye (1995) present two algorithms for quadrilateral mesh refinement. These algorithms refine quadrilateral meshes while maintaining mesh conformity. The first algorithm maintains conformity by introducing triangles. The second algorithm maintains conformity without triangles, but requires a larger degree of refinement. Both algorithms introduce nodes with non-optimal valences. ...