NEW PROGRESS IN REDUCED ELEMENT: AN ADAPTIVE FINITE ELEMENT METHOD WITH BUILT-IN ERROR ESTIMATOR IN MAXIMUM NORM

Based on the successful performance of the reduced element for initial value problems, the reduced element for general boundary value problems is proposed without the needs for super-convergence calculations, structural meshes and nodal accuracy improvement. An adaptive finite element algorithm with the solution of the reduced element and a built-in maximum norm error estimator as the final results is subsequently proposed. This paper gives a brief report to this research progress and provides preliminary numerical examples in one- and two-dimensional boundary value problems to exhibit the feasibility, effectiveness and reliability of the proposed algorithm.