Higher order approximation of biharmonic problem using the WEB-Spline based mesh-free method
Authors :- Rajashekar Naraveni, Sudhakar Chaudhary, Srinivas Kumar VVK
Publication :- International Journal of Nonlinear Sciences and Numerical Simulation, May 2021.
In this paper, we consider a biharmonic equation with Navier boundary conditions and we decoupled this fourth order biharmonic equation into a system of second order equations. In numerics, there is an advantage because of this decoupling, i.e., one can use C0 finite elements to solve the decoupled system instead of C1 finite elements. For solving this decoupled system of second order equations, we use the weighted extended b-spline (WEB-Spline) based mesh-free finite element method. The WEB-Spline method does not require any mesh generation and eliminates the difficult, time-consuming preprocessing step. Also, by the WEB-Spline method higher order approximations are possible with relatively low dimensional spaces. Numerical results based on the WEB-Spline method are compared with the usual finite element method in order to demonstrate the efficiency of the proposed method.