Approximation of elliptic equations with BMO coefficients (Q2794703)

The authors study the convergence of the finite element method to approximately solving the boundary value problem NEWLINE\[NEWLINE \nabla (A(x)\nabla u) = \nabla f \qquad \text{in} \quad\Omega,\qquad U|_{\partial\Omega}=0,NEWLINE\]NEWLINE where the bounded domain \( \Omega \subset \mathbb R^{d}\) \(( d \geq 1)\) has the Lipschitz boundary \( \partial\Omega \) and \(f\in L^{p}(\Omega)\). A particular case is considered, when the entries of the positive definite matrix \( A \) have bounded mean oscillation (BMO). This notion, the weak and strong convergence of approximate solutions are reproduced from the results of several articles cited in the references.