A 𝐶⁰-IP method for distributed optimal control problem governed by a non-divergent form PDE with Cordes coefficients

In this article, we develop a quadratic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Superscript 0"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>0</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">C^{0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> interior penalty method for the distributed optimal control problem governed by a second order elliptic partial differential equation (PDE) in nondivergence form. We derive both a priori and a posteriori error estimates. The theoretical results are illustrated by numerical experiments.