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New a posteriori L ( L 2 ) and L 2 ( L 2 ) -error estimates of mixed finite element methods for general nonlinear parabolic optimal control problems

Zuliang Lu (2016)

Applications of Mathematics

We study new a posteriori error estimates of the mixed finite element methods for general optimal control problems governed by nonlinear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates in L ( J ; L 2 ( Ω ) ) -norm and L 2 ( J ; L 2 ( Ω ) ) -norm for both the state, the co-state and the control approximation. Such estimates, which seem to be new, are an important...

New efficient numerical method for 3D point cloud surface reconstruction by using level set methods

Kósa, Balázs, Haličková-Brehovská, Jana, Mikula, Karol (2017)

Proceedings of Equadiff 14

In this article, we present a mathematical model and numerical method for surface reconstruction from 3D point cloud data, using the level-set method. The presented method solves surface reconstruction by the computation of the distance function to the shape, represented by the point cloud, using the so called Fast Sweeping Method, and the solution of advection equation with curvature term, which creates the evolution of an initial condition to the final state. A crucial point for efficiency is...

New Einstein metrics on Sp ( n ) which are non-naturally reductive

Shaoxiang Zhang, Huibin Chen (2022)

Czechoslovak Mathematical Journal

We prove that there are at least two new non-naturally reductive Ad ( Sp ( l ) × Sp ( k ) × Sp ( k ) × Sp ( k ) ) invariant Einstein metrics on Sp ( l + 3 k ) ( k < l ) . It implies that every compact simple Lie group Sp ( n ) ...

New estimates and tests of independence in semiparametric copula models

Salim Bouzebda, Amor Keziou (2010)

Kybernetika

We introduce new estimates and tests of independence in copula models with unknown margins using φ -divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the parameter is an interior or a boundary value of the parameter space. Simulation results show that the choice of χ 2 -divergence has good properties in terms of efficiency-robustness.

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