Related papers: A second-order face-centred finite volume method o…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…
In this paper, a parameter-uniform fitted mesh finite difference scheme is constructed and analyzed for a class of singularly perturbed interior turning point problems. The solution of this class of turning point problem possess two outflow…
The approximation properties of the finite element method can often be substantially improved by choosing smooth high-order basis functions. It is extremely difficult to devise such basis functions for partitions consisting of arbitrarily…
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…
In this paper, we analyze vertex-centered finite volume method (FVM) of any order for elliptic equations on rectangular meshes. The novelty is a unified proof of the inf-sup condition, based on which, we show that the FVM approximation…
The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…
This paper makes the first attempt to apply newly developed upwind GFDM for the meshless solution of two-phase porous flow equations. In the presented method, node cloud is used to flexibly discretize the computational domain, instead of…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the…
We consider a finite volume method for a well-driven fluid flow in a porous medium. Due to the singularity of the well, modeling in the near-well region with standard numerical schemes results in a completely wrong total well flux and an…
We consider a class of nonconvex nonsmooth optimization problems whose objective is the sum of a smooth function and a finite number of nonnegative proper closed possibly nonsmooth functions (whose proximal mappings are easy to compute),…
Many engineering systems require accurate simulations of complex physical systems. Yet, analytical solutions are only available for simple problems, necessitating numerical approximations such as the Finite Element Method (FEM). The cost…
We consider the problem of obese human mesh recovery, i.e., fitting a parametric human mesh to images of obese people. Despite obese person mesh fitting being an important problem with numerous applications (e.g., healthcare), much recent…
The main contribution of this paper is the formulation of a diffuse approximation method(DAM), for two-dimensional channel flows. The proposed method is based on the vorticity-streamfunction formulation. The DAM which estimates derivates of…
We consider second-order PDE problems set in unbounded domains and discretized by Lagrange finite elements on a finite mesh, thus introducing an artificial boundary in the discretization. Specifically, we consider the reaction diffusion…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
The softmax-based loss functions and its variants (e.g., cosface, sphereface, and arcface) significantly improve the face recognition performance in wild unconstrained scenes. A common practice of these algorithms is to perform…
An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…
Convergence failure and slow convergence rates are among the biggest challenges with solving the system of non-linear equations numerically. Although mitigated, such issues still linger when using strictly small time steps and…