Special quadratic quadrilateral finite elements for local refinement with irregular nodes Original Research Article

For the finite element method, a new approach has been developed to treat quadratic quadrilateral elements at the interface of different refinement levels. The local refinement is performed with special quadrilateral elements. Irregular nodes are eliminated and at the same time the local continuity at inter-elements is preserved. The new method is accurate, easy to implement and shows good efficiency for local refinement with quadrilateral elements. The special elements can be used for solving Navier–Stokes equations and reactive flow problems. They show great potential for solving combustion problems with moving flame fronts and complex or moving boundaries.