相关论文: Linking ghost penalty and aggregated unfitted meth…

This paper studies the stability of velocity-pressure mixed approximations of the Stokes problem when different finite element (FE) spaces for each component of the velocity field are considered. We consider some new combinations of…

We consider the reliable implementation of high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their…

In this work, we study the task of distributed optimization over a network of learners in which each learner possesses a convex cost function, a set of affine equality constraints, and a set of convex inequality constraints. We propose a…

A majorized accelerated block coordinate descent (mABCD) method in Hilbert space is analyzed to solve a sparse PDE-constrained optimization problem via its dual. The finite element approximation method is investigated. The attractive…

A new family of penalty functions, adaptive to likelihood, is introduced for model selection in general regression models. It arises naturally through assuming certain types of prior distribution on the regression parameters. To study…

In this paper we study the loss of precision of numerical methods discretizing anisotropic problems and propose alternative approaches free from this drawback. The deterioration of the accuracy is observed when the coordinates and the mesh…

This work studies discontinuous Galerkin (DG) approximations of the boundary value problem for homogeneous transversely isotropic linear elastic bodies. Low-order approximations on triangles are adopted, with the use of three interior…

We develop a new numerical technique for approximating solutions of the Navier-Stokes equations on moving domains. The method aims at simulating an incompressible fluid past an object whose motion is assigned a priori using a level-set…

In this paper we introduce and analyze the residual-based a posteriori error estimation of the partially penalized immersed finite element method for solving elliptic interface problems. The immersed finite element method can be naturally…

In this work, we propose the joint use of a mixed penalty-interior point method and direct search, for addressing nonlinearly constrained derivative-free optimization problems. A merit function is considered, wherein the set of nonlinear…

Near-optimal computational complexity of an adaptive stochastic Galerkin method with independently refined spatial meshes for elliptic partial differential equations is shown. The method takes advantage of multilevel structure in expansions…

We develop and analyze a posteriori error estimators for a proper orthogonal decomposition-discrete empirical interpolation method (Pod-Deim) reduced order model applied to a parametric Poisson equation posed on a parameter-dependent domain…

We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove convergence of an…

Our recent study (Lin and Ohtsuka, 2024) proposed a new penalty method for solving mathematical programming with complementarity constraints (MPCC). This method first reformulates MPCC as a parameterized nonlinear programming called gap…

In this paper we consider a class of structured nonsmooth difference-of-convex (DC) constrained DC program in which the first convex component of the objective and constraints is the sum of a smooth and nonsmooth functions while their…

In this paper we propose a penalized Crouzeix-Raviart element method for eigenvalue problems of second order elliptic operators. The key idea is to add a penalty term to tune the local approximation property and the global continuity…

In this work, the joint use of a mixed penalty-interior point method and direct search is proposed, to address {nonlinear} constrained derivative-free optimization problems. A merit function is considered, wherein the set of nonlinear…

We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…

A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the a posteriori error estimation framework introduced by…

We present a general theory of exact penalty functions with vectorial (multidimensional) penalty parameter for optimization problems in infinite dimensional spaces. In comparison with the scalar case, the use of vectorial penalty parameters…