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A POSTERIORI ERROR CONTROL FOR NONCONVEX PROBLEMS VIA CALIBRATION
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AI
DOI：10.1137/25M1782959.png)
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Abstract
En 中文
In this paper, a posteriori error estimates are derived for the approximation error of minimizers of functionals on the space of functions with bounded variation with a nonconvex lowerPartial Differential Equations, 16 (2003), pp. 299--333] allows the problem to be reformulated as a uniformly convex variational problem over characteristic functions of subgraphs in one dimension higher. A primal-dual approach is formulated where the duality of divergence and gradient properly incorporates boundary conditions for the primal variable. Based on this, a posteriori error estimates can be derived first for the relaxed problem in the L2-norm. A cut-out argument allows converting this into an L1-error estimate for the characteristic subgraph functions apart from the jump interface, whereas the area of the interfacial region is estimated separately. To apply the estimate, we consider as one possible discretization a conforming finite element space for the primal variable and a nonconforming space for the dual variable. Finally, we validate the a posteriori error estimates in numerical experiments for a prototypical nonconvex functional in one and two dimensions as well as depth estimation in stereo imaging, a classical computer vision problem.
Keywords:
variational methods
a posteriori error control
calibrations
finite elements
Journal
IF:
2.9
Papers:
29
Citations:
1.5W