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  1. A nonlinear least-squares finite element method for strong solutions of the Dirichlet boundary value problem of a two-dimensional Pucci equation on convex polygonal domains is investigated in this paper. We obtain a priori and a posteriori error estimates and present corroborating numerical results, where the discrete nonsmooth and nonlinear optimization problems are solved by an active set method and an alternating direction method with multipliers. 
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    Free, publicly-accessible full text available April 26, 2025
  2. We consider C0 interior penalty methods for a linear-quadratic elliptic distributed optimal control problem with pointwise state constraints in two spatial dimensions, where the cost function tracks the state at points, curves and regions of the domain. Error estimates and numerical results that illustrate the performance of the methods are presented. 
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    Free, publicly-accessible full text available February 1, 2025
  3. We present an adaptive nonlinear least-squares finite element method for a two dimensional Pucci equation. The efficiency of the method is demonstrated by a numerical experiment. 
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  4. Abstract

    We construct a symmetric interior penalty method for an elliptic distributed optimal control problem with pointwise state constraints on general polygonal domains.The resulting discrete problems are quadratic programs with simple box constraints that can be solved efficiently by a primal-dual active set algorithm.Both theoretical analysis and corroborating numerical results are presented.

     
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  5. We establish an interior maximum norm error estimate for the symmetric interior penalty method on planar polygonal domains. 
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  6. We design and analyze a [Formula: see text] virtual element method for an elliptic distributed optimal control problem with pointwise state constraints. Theoretical estimates and corroborating numerical results are presented. 
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