ELEMENTWISE DECOMPOSITION OF A POSTERIORI ERRORESTIMATOR BASED ON REFERENCE SOLUTION FOR HP-ADAPTIVE FINITE ELEMENT METHOD

Анотація

We consider the construction of a posteriori error estimator (AEE), based on the reference solution for one-dimensional hp-adaptive finite element method (FEM). It is shown that the square of the global error estimator can be represented as a sum of squares of single element error indicators, which are calculated independently on the elements of the selected mesh. The obtained decomposition can be used to justify the iterative algorithms of hp-adaptive FEM schemes. The proposed estimator can be used to calculate the error decrease rates for different local mesh refinement of just single finite element without re-calculating the entire reference solution on the whole problem domain. In addition, by choosing the system of Lobatto functions as a finite element basis, we propose an efficient scheme for calculating the local indicators.
Key words: finite element method, Galerkin method, orthogonal projection, Lobatto basis, Green’s function, hp-adaptivity, a posteriori error estimator, well posed problem, diffusion-advection-reaction boundary value problem, reference solution.