Mixed Meshless Local Petrov-Galerkin Methods for Solving Linear Fourth-Order Differential Equations

The paper presents meshless methods based on the mixed Meshless Local Petrov-Galerkin approach used for solving linear fourth-order differential equations. In all the methods presented here, the primary variable and its derivatives up to the third order are approximated separately. Three different mixed meshless methods are derived by different choices of test and trial functions and are verified using available analytical and reference solutions. The numerical performance of the presented algorithms is demonstrated by several representative numerical examples