Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A Mixed Finite Element Scheme for Optimal Control Problems with Pointwise State Constraints
Journal of Scientific Computing
A Sign Preserving Mixed Finite Element Approximation for Contact Problems
International Journal of Applied Mathematics and Computer Science - Issues in Advanced Control and Diagnosis
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We consider finite element, operators defined on "rough" functions in a bounded polyhedron Ω in RN. Insisting on preserving positivity in the approximations, we discover an intriguing and basic difference between approximating functions which vanish on the boundary of Ω and approximating general functions which do not. We give impossibility results for approximation of general functions to more than first order accuracy at extreme points of Ω. We also give impossibility results about invariance of positive operators on finite element functions. This is in striking contrast to the well-studied case without positivity.