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Although these methods are formally first-order accurate when a shock is present, they still have uniform high-order accuracy right up to the shock location. In this paper, we propose a novel third-order numerical method for solving optimal control problems subject to scalar nonlinear hyperbolic conservation laws. It is based on the first-disretize-then-optimize approach and combines a discrete adjoint WENO scheme of third order with the classical strong stability preserving three-stage third-order Runge\u2013Kutta method SSPRK3. We analyze its approximation properties and apply it to optimal control problems of tracking-type with non-smooth target states. Comparisons to common first-order methods such as the Lax\u2013Friedrichs and Engquist\u2013Osher method show its great potential to achieve a higher accuracy along with good resolution around discontinuities.<\/jats:p>","DOI":"10.1007\/s10589-021-00295-2","type":"journal-article","created":{"date-parts":[[2021,7,2]],"date-time":"2021-07-02T11:07:16Z","timestamp":1625224036000},"page":"301-320","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A third-order weighted essentially non-oscillatory scheme in optimal control problems governed by nonlinear hyperbolic conservation laws"],"prefix":"10.1007","volume":"80","author":[{"given":"David","family":"Frenzel","sequence":"first","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0003-4603-6554","authenticated-orcid":false,"given":"Jens","family":"Lang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,7,2]]},"reference":[{"key":"295_CR1","unstructured":"Aguilar, S.P., Schmitt, J.M., Ulbrich, S., Moos, M.: On the numerical discretization of optimal control problems for conservation laws. 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