Related papers: Multi-level structured deformations: relaxation vi…
An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh deformation technique (MDT) used to adapt the computational mesh in the moving fluid domain. An ideal technique is computationally…
A transient analysis to quantify droplet deformation under DC electric fields is presented. The full Taylor-Melcher leaky dielectric model is employed where the charge relaxation time is considered to be finite. The droplet is assumed to be…
We develop a finite element method for a large deformation membrane elasticity problem on meshed surfaces using a tangential differential calculus approach that avoids the use of classical differential geometric methods. The method is also…
Multi-view methods learn representations by aligning multiple views of the same image and their performance largely depends on the choice of data augmentation. In this paper, we notice that some other useful augmentations, such as image…
We prove integrated local energy decay for the damped wave equation on stationary, asymptotically flat space-times in (1 + 3) dimensions. Local energy decay constitutes a powerful tool in the study of dispersive partial differential…
With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent…
This article gives a ``fundamental solution'' based energy-norm harmonic interpolation approach for two half-space settings of interest: the upper-half $\mathbb{R}^n$ plane, where fundamental solutions satisfy Laplace's equation, and the…
We show that classical molecular density functional theory (MDFT), here in the homogeneous reference fluid approximation in which the functional is inferred from the properties of the bulk solvent, is a powerful new tool to study, at a…
The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of…
We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…
Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…
Solution of the momentum space Schr\"odinger equation in the case of deformed fields is being addressed. In particular it is shown that a complete set of single particle states which includes bound, resonant and complex continuum states may…
We give a necessary and sufficient condition, of geometric type, for the uniform decay of energy of solutions of the linear system of magnetoelasticity in a bounded domain with smooth boundary. A Dirichlet-type boundary condition is…
We consider systematic numerical approximation of a viscoelastic phase separation model that describes the demixing of a polymer solvent mixture. An unconditionally stable discretisation method is proposed based on a finite element…
This paper presents a framework for the analysis of discretization methods based on the decomposition into local and global problems. We apply the framework to provide a comprehensive error analysis for the embedded Trefftz discontinuous…
In this paper, we prove the global existence of strong solutions for the inhomogeneous incompressible viscoelastic system without any additional structure assumptions on $\mathbb{R}^{3}$. Unlike the time weighted energy method presented by…
A variational approach to the reconstruction of a shape (2D simple manifolds) as triangulated surface from given level set using shape gradients is presented. It involves an energy functional that depends on the local shape characteristics…
In this paper, we propose and analyze an abstract stabilized mixed finite element framework that can be applied to nonlinear incompressible elasticity problems. In the abstract stabilized framework, we prove that any mixed finite element…
Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…
We consider (locally) energy finite coordinates associated with a strongly local regular Dirichlet form on a metric measure space. We give coordinate formulas for substitutes of tangent spaces, for gradient and divergence operators and for…