Explicit a posteriori local error estimation for FEM solutions
Provides explicit local error bounds for finite element solutions, which is useful for adaptive mesh refinement in computational engineering.
The paper proposes a local a posteriori error estimation method for FEM solutions of Poisson's equation based on the Hypercircle method, which works even without H^2 regularity. Numerical experiments on 2D and 3D domains demonstrate its efficiency.
For the finite element solution of Poisson's equation, a local a posteriori error estimation based on the Hypercircle method is proposed. Even for the solution of Poisson's equation without the $H^2$ regularity, this method can provide explicit local error estimation. The efficiency of the proposed method is demonstrated by numerical experiments for the boundary value problem of Poisson's equation defined on the 2D and 3D domains.