Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
On the finite element method for mixed variational inequalities arising in elastoplasticity
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Quadratic finite element approximation of the Signorini problem
Mathematics of Computation
Mixed finite element methods for unilateral problems: convergence analysis and numerical studies
Mathematics of Computation
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We present a free-locking finite element approximation of the displacement-pressure formulation for the Signorini problem, in nearly incompressible elasticity. Studying the nonlinear variational problem requires an appropriate saddle point theory. An abstract framework is laid down and applied to the system of the variational inequalities we are involved in. Existence and uniqueness results for the continuous problem are proven and optimal convergence rates of the mixed Taylor-Hood finite element discretisation are proved. Some numerical experiences are reported to underline the reliability of this approach.