Related papers: An interface-unfitted finite element method for el…
We consider a numerical approximation of a linear quadratic control problem constrained by the stochastic heat equation with non-homogeneous Neumann boundary conditions. This involves a combination of distributed and boundary control, as…
We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…
We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The…
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate…
This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated…
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…
For the first time, a nonlinear interface problem on an unbounded domain with nonmonotone set-valued transmission conditions is analyzed. The investigated problem involves a nonlinear monotone partial differential equation in the interior…
This article presents an error analysis of the recently introduced Frenet immersed finite element (IFE) method. The Frenet IFE space employed in this method is constructed to be locally conforming to the function space of the associated…
This article presents an error analysis of the symmetric linear/bilinear partially penalized immersed finite element (PPIFE) methods for interface problems of Helmholtz equations. Under the assumption that the exact solution possesses a…
We formulate and analyze a Nitsche-type algorithm for frictional contact problems. The method is derived from, and analyzed as, a stabilized finite element method and shown to be quasi-optimal, as well as suitable as an adaptive scheme…
We propose a new finite element method for Helmholtz equation in the situation where an acoustically permeable interface is embedded in the computational domain. A variant of Nitsche's method, different from the standard one, weakly…
In this paper, we present a new numerical method for determining the numerical solution of interface problems to optimal accuracy with respect to the polynomial order of the Lagrangian finite element space on polytopial meshes. We introduce…
In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to…
We present a weak finite element method for elliptic problems in one space dimension. Our analysis shows that this method has more advantages than the known weak Galerkin method proposed for multi-dimensional problems, for example, it has…
In this paper we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element discretization of arbitrary order of accuracy for biharmonic…
This paper is concerned with finite element error estimates for Neumann boundary control problems posed on convex and polyhedral domains. Different discretization concepts are considered and for each optimal discretization error estimates…
In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…
In this paper, we propose a novel high order unfitted finite element method on Cartesian meshes for solving the acoustic wave equation with discontinuous coefficients having complex interface geometry. The unfitted finite element method…
Immersed finite element (IFE) methods are a group of long-existing numerical methods for solving interface problems on unfitted meshes. A core argument of the methods is to avoid mesh regeneration procedure when solving moving interface…
We present a multigrid method for an unfitted finite element discretization of the Dirichlet boundary value problem. The discretization employs Nitsche's method to implement the boundary condition and additional face based ghost penalties…