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• Asymptotic mean value formulas for parabolic nonlinear equations 

  Blanc, Pablo; Charro, Fernando; Manfredi, Juan J.; Rossi, Julio D. (Union Matematica Argentina, 2022)

  In this paper we characterize viscosity solutions to nonlinear parabolic equations (including parabolic Monge–Ampère equations) by asymptotic mean value formulas. Our asymptotic mean value formulas can be interpreted from ...

• Bounds for the solution of a system of parabolic equations arising in circuit theory 

  Marinov, Corneliu A.; Neittaanmäki, Pekka; Santanen, Jukka-Pekka (North-Holland, 1992)

  The modelling of the influence of interconnections on the delay time in MOS integrated circuits leads to a system of parabolic equations coupled by boundary conditions given in the form of the ordinary differential equation ...

• Guaranteed lower bounds for cost functionals of time-periodic parabolic optimization problems 

  Wolfmayr, Monika (Elsevier, 2020)

  In this paper, a new technique is shown for deriving computable, guaranteed lower bounds of functional type (minorants) for two different cost functionals subject to a parabolic time-periodic boundary value problem. Together ...

• Functional Type Error Control for Stabilised Space-Time IgA Approximations to Parabolic Problems 

  Langer, Ulrich; Matculevich, Svetlana; Repin, Sergey (Springer International Publishing, 2018)

  The paper is concerned with reliable space-time IgA schemes for parabolic initial-boundary value problems. We deduce a posteriori error estimates and investigate their applicability to space-time IgA approximations. ...

• Guaranteed error bounds and local indicators for adaptive solvers using stabilised space-time IgA approximations to parabolic problems 

  Langer, Ulrich; Matculevich, Svetlana; Repin, Sergey (Elsevier, 2019)

  The paper is concerned with space–time IgA approximations to parabolic initial–boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of such type of approximations and ...