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Numerical analysis of a finite element/volume penalty method. (English) Zbl 1191.65157

Some standard properties of the penalty method in the framework of constrained quadratic minimization including some facts about the space discretization of prblems are presented. The author gives an abstract estimate for primal and dual parts of the discretized/penalized problem. On a model problem in the spirit of fluid-particle flows is showed how the abstract estimate can be applied.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
49M30 Other numerical methods in calculus of variations (MSC2010)
65N08 Finite volume methods for boundary value problems involving PDEs
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