A-posteriori reduced basis error-estimates for a semi-discrete in space quasilinear parabolic PDE

Fabian Hoppe () and Ira Neitzel ()
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Fabian Hoppe: Rheinische Friedrich-Wilhelms-Universität Bonn
Ira Neitzel: Rheinische Friedrich-Wilhelms-Universität Bonn

Computational Optimization and Applications, 2024, vol. 87, issue 3, No 4, 755-784

Abstract: Abstract We prove a-posteriori error-estimates for reduced-order modeling of quasilinear parabolic PDEs with non-monotone nonlinearity. We consider the solution of a semi-discrete in space equation as reference, and therefore incorporate reduced basis-, empirical interpolation-, and time-discretization-errors in our consideration. Numerical experiments illustrate our results.

Keywords: Quasilinear parabolic partial differential equation; Reduced basis; Proper Orthogonal Decomposition; A-posteriori error; 35K59; 65M15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-021-00299-y

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