Optimization with Partial Differential Equations
نویسندگان
چکیده
The fundamental solution of the Laplace equation in two dimensions is not contained in the Sobolev space H1(Ω) such that finite element error estimates are non-standard and quasi-uniform meshes are inappropriate. By using graded meshes L2-error estimates of almost optimal order are shown. As a by-product, we show for the Poisson equation with a right-hand side in L2 that appropriate mesh refinement near some interior point diminishes the error in this point by nearly one order.
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