Adaptive finite element methods (AFEM) represent a pivotal advancement in numerical analysis by dynamically refining computational meshes to achieve greater solution accuracy. These methods are ...

We propose an adaptive finite element method for linear elliptic problems based on an optimal maximum norm error estimate. The algorithm produces a sequence of ...

SIAM Journal on Numerical Analysis, Vol. 42, No. 5 (2005), pp. 2188-2217 (30 pages) Although existing adaptive finite element methods for solving second order elliptic equations often perform better ...

Abstract: A key consideration in the design of supersonic aircraft is reducing the effects of sonic boom. In the past 15 years, significant progress has led to the demonstration of geometric shaping ...

What Are FEM, FDM and FVM? FEM, FDM and FVM differ from one another in important ways. Understanding these distinctions is key to selecting the method most appropriate for your purposes. The ...