Residual error estimate for BEM-based FEM on polygonal meshes (Q635810)

The author studies a finite element method (FEM) to solve the boundary value problem \[ -\text{div}(a(x)\nabla u(x))= f(x),\quad x\in\Omega\subset \mathbb R^{2}, \] where \(\Omega\) is a polygonal Lipschitz domain with the boundary \(\Gamma=\Gamma_{D}\cup \Gamma _{N}\). The mesh on this domain is constructed also in polygonal form, that fulfills more conditions. The error estimate of this method uses a so called ``residual error'' on the edges of the element mesh.