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García, Carlos; Gatica, Gabriel N.; Meddahi, Salim
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1 Citations
We provide a new mixed finite element analysis for linear elastodynamics with reduced symmetry. The problem is formulated as a second order system in time by imposing only the Cauchy stress tensor and the rotation as primary and secondary variables, respectively. We prove that the resulting variational formulation is wellposed and provide a convergence analysis for a class of
$${\mathrm {H}}(\mathop {{\mathrm {div}}}\nolimits )$$
conforming semidiscrete schemes. In addition, we use the Newmark trapezoidal rule to obtain a fully discrete version of the problem and carry out the corresponding convergence analysis. Finally, numerical tests illustrating the performance of the fully discrete scheme are presented.
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Yuan, Yirang
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Abstract
For a coupled system of multiplayer dynamics of fluids in porous media, the characteristic finite element domain decomposition procedures applicable to parallel arithmetic are put forward. Techniques such as calculus of variations, domain decomposition, characteristic method, negative norm estimate, energy method and the theory of prior estimates are adopted. Optimal order estimates in L^{2} norm are derived for the error in the approximate solution.
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Boffi, Daniele; Gastaldi, Lucia
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5 Citations
We study a recently introduced formulation for fluidstructure interaction problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method. The time discretization of the problem leads to a mixed problem for which a rigorous stability analysis is provided. The finite element space discretization is discussed and optimal convergence estimates are proved.
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Brenner, Susanne C.; Neilan, Michael; Sung, LiYeng
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9 Citations
In this paper we develop isoparametric C^{0} interior penalty methods for plate bending problems on smooth domains. The orders of convergence of these methods are shown to be optimal in the energy norm. We also consider the convergence of these methods in lower order Sobolev norms and discuss subparametric C^{0} interior penalty methods. Numerical results that illustrate the performance of these methods are presented.
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Wang, Cheng; Huang, Ziping; Li, Likang
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8 Citations
A twogrid partition of unity method for second order elliptic problems is proposed and analyzed. The standard twogrid method is a local and parallel method usually leading to a discontinuous solution in the entire computational domain. Partition of unity method is employed to glue all the local solutions together to get the global continuous one, which is optimal in H^{1}norm. Furthermore, it is shown that the L^{2} error can be improved by using the coarse grid correction. Numerical experiments are reported to support the theoretical results.
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Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
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14 Citations
In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in Gillette et al. (Adv Comput Math 37(3), 417–439, 2012), we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter one satisfying certain simple geometric restrictions. This work makes rigorous an observed practical advantage of the mean value coordinates: unlike Wachspress coordinates, the gradients of the mean value coordinates do not become large as interior angles of the polygon approach π.
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Araya, Rodolfo; Poza, Abner H.; Valentin, Frédéric
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2 Citations
This work proposes and analyses an adaptive finite element scheme for the fully nonlinear incompressible NavierStokes equations. A residual a posteriori error estimator is shown to be effective and reliable. The error estimator relies on a Residual Local Projection (RELP) finite element method for which we prove wellposedness under mild conditions. Several wellestablished numerical tests assess the theoretical results.
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Krause, Rolf; Veeser, Andreas; Walloth, Mirjam
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6 Citations
We derive a new a posteriori error estimator for the Signorini problem. It generalizes the standard residualtype estimators for unconstrained problems in linear elasticity by additional terms at the contact boundary addressing the nonlinearity. Remarkably these additional contactrelated terms vanish in the case of socalled fullcontact. We prove reliability and efficiency for two and threedimensional simplicial meshes. Moreover, we address the case of nondiscrete gap functions. Numerical tests for different obstacles and starting grids illustrate the good performance of the a posteriori error estimator in the two and threedimensional case, for simplicial as well as for unstructured mixed meshes.
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By
Shi, Dongyang; Xu, Chao
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2 Citations
The nonconforming CrouzeixRaviart type linear triangular finite element approximate to secondorder elliptic problems is studied on anisotropic general triangular meshes in 2D satisfying the maximal angle condition and the coordinate system condition. The optimalorder error estimates of the broken energy norm and L^{2}norm are obtained.
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Boulmezaoud, Tahar Z.; Kaliche, Keltoum; Kerdid, Nabil
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1 Citations
We use inverted finite element method (IFEM) for computing threedimensional vector potentials and for solving divcurl systems in the whole space
$\mathbb {R}^{3}$
. IFEM is substantially different from the existing approaches since it is a non truncature method which preserves the unboundness of the domain. After developping the method, we analyze its convergence in term of weighted norms. We then give some threedimensional numerical results which demonstrate the efficiency and the accuracy of the method and confirm its convergence.
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