Finite-Element Approximation of Elliptic Equations with a Neumann or Robin Condition on a Curved Boundary
نویسندگان
چکیده
This paper considers a finite-element approximation of a second-order selfadjoint elliptic equation in a region flcR" (with n = 2 or 3) having a curved boundary dQ on which a Neumann or Robin condition is prescribed. If the finite-element space denned over D, a union of elements, has approximation power h in the L norm, and if the region of integration is approximated by Q* with dist (Q, £?*) =£ Ch, then it is shown that one retains optimal rates of convergence for the error in the H and L norms, whether Q* is fitted (£^ = D) or unfitted (Q* c £>*), provided that the numerical integration scheme has sufficient accuracy.
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