Numerical approximation of young measuresin non-convex variational problems

2000 ◽  
Vol 84 (3) ◽  
pp. 395-415 ◽  
Author(s):  
Carsten Carstensen ◽  
Tomáš Roubíček
Keyword(s):  
Numerical Approximation ◽  
Variational Problems ◽  
Convex Variational Problems

scholarly journals Duality for non-convex variational problems

2015 ◽  
Vol 353 (4) ◽  
pp. 375-379 ◽  
Author(s):  
Guy Bouchitté ◽  
Ilaria Fragalà
Keyword(s):  
Variational Problems ◽  
Convex Variational Problems

scholarly journals Reliable Numerical Solution of a Class of Nonlinear Elliptic Problems Generated by the Poisson–Boltzmann Equation

2020 ◽  
Vol 20 (2) ◽  
pp. 293-319 ◽  
Author(s):  
Johannes Kraus ◽  
Svetoslav Nakov ◽  
Sergey I. Repin
Keyword(s):  
Boltzmann Equation ◽  
Elliptic Problems ◽  
Variational Problems ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Approximation Errors ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
2D And 3D ◽  
Convex Variational Problems

AbstractWe consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson–Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in [19] for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computable majorants and minorants of the global error as well as indicators of local errors that provide efficient adaptation of meshes. Theoretical results are confirmed by a collection of numerical tests that includes problems on 2D and 3D Lipschitz domains.

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