In this paper, we study the stability of the nonsymmetric version of Nitsche's method without penalty for compressible and incompressible elasticity. For the compressible case we prove the convergence of the error in the H 1 -and L 2 -norms. In the incompressible case we use a Galerkin least squares pressure stabilization and we prove the convergence in the H 1 -norm for the velocity and convergence of the pressure in the L 2 -norm.
In this paper, we consider a fictitious domain approach based on a Nitsche type method without penalty. To allow for high order approximation using piecewise affine approximation of the geometry we use a boundary value correction technique based on Taylor expansion from the approximate to the physical boundary. To ensure stability of the method a ghost penalty stabilization is considered in the boundary zone. We prove optimal error estimates in the H 1 -norm and estimates suboptimal by Oph 1 2 q in the L 2norm. The suboptimality is due to the lack of adjoint consistency of our formulation. Numerical results are provided to corroborate the theoretical study.
We devise a space-time tensor method for the low-rank approximation of linear parabolic evolution equations. The proposed method is a stable Galerkin method, uniformly in the discretization parameters, based on a Minimal Residual formulation of the evolution problem in Hilbert-Bochner spaces. The discrete solution is sought in a linear trial space composed of tensors of discrete functions in space and in time and is characterized as the unique minimizer of a discrete functional where the dual norm of the residual is evaluated in a space semi-discrete test space. The resulting global space-time linear system is solved iteratively by a greedy algorithm. Numerical results are presented to illustrate the performance of the proposed method on test cases including non-selfadjoint and time-dependent differential operators in space. The results are also compared to those obtained using a fully discrete Petrov-Galerkin setting to evaluate the dual residual norm.
We propose a forecasting method for predicting epidemiological health series on a twoweek horizon at the regional and interregional level. The approach is based on model order reduction of parametric compartmental models, and is designed to accommodate small amount of sanitary data. The efficiency of the method is examined in the case of the prediction of the number of hospitalized infected and removed people during the first pandemic wave of COVID-19 in France, which has taken place approximately between February and May 2020. Numerical results illustrate the promising potential of the approach.
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