Related papers: Numerical analysis for the Stokes problem with non…
This paper derives optimal coefficients for optimized Schwarz iterations for the time-dependent Stokes-Darcy problem using an innovative strategy to solve a nonstandard min-max problem. The coefficients take into account both physical and…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
The aim of this paper is to study the shape optimization method for solving the Bernoulli free boundary problem, a well-known ill-posed problem that seeks the unknown free boundary through Cauchy data. Different formulations have been…
We present an approach to handle Dirichlet type nonlocal boundary conditions for nonlocal diffusion models with a finite range of nonlocal interactions. Our approach utilizes a linear extrapolation of prescribed boundary data. A novelty is,…
The paper deals with the Stokes problem, associated with a flow of a viscous incompressible fluid through a spatially periodic profile cascade. We use results from [32] (the maximum regularity property in the $L^2$-framework) and [33] (the…
In this work we study an optimal control problem subject to the instationary Navier-Stokes equations, where the control enters via an inhomogeneous Neumann/Do-Nothing boundary condition. Despite the Navier-Stokes equations with these…
We study qualitative properties of initial traces of nonnegative solutions to a semilinear heat equation in a smooth domain under the Dirichlet boundary condition. Furthermore, for the corresponding Cauchy--Dirichlet problem, we obtain…
In this article, we analyse a stabilised equal-order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a sub-domain, for example along the boundary of the domain,…
In this paper we introduce new characterizations of spectral fractional Laplacian to incorporate nonhomogeneous Dirichlet and Neumann boundary conditions. The classical cases with homogeneous boundary conditions arise as a special case. We…
In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner.~We first derive continuous energy estimates,~and then proceed to the discrete setting.~We formulate…
We introduce a novel monotone discretization method for addressing obstacle problems involving the integral fractional Laplacian with homogeneous Dirichlet boundary conditions over bounded Lipschitz domains. This problem is prevalent in…
In this paper we consider the stability and convergence of numerical discretizations of the Black-Scholes partial differential equation (PDE) when complemented with the popular linear boundary condition. This condition states that the…
A general regularization strategy is considered for the efficient iterative solution of the lowest-order weak Galerkin approximation of singular Stokes problems. The strategy adds a rank-one regularization term to the zero (2,2) block of…
This work develops an efficient and accurate optimization algorithm to study the optimal mixing problem driven by boundary control of unsteady Stokes flows, based on the theoretical foundation laid by Hu and Wu in a series of work. The…
We study the long-time dynamics of the nonlinear processes modeled by diffusion-transport partial differential equations in non-divergence form with drifts. The solutions are subject to some inhomogeneous Dirichlet boundary condition.…
The Blackstock-Crighton equation models nonlinear acoustic wave propagation in thermo-viscous fluids. In the present work we investigate the associated inhomogeneous Dirichlet and Neumann boundary value problems in a bounded domain and…
This paper is devoted to the well-posedness analysis of a nonstationary Stokes hemivariational inequality for an incompressible fluid flow described by the Stokes equations subject to a nonsmooth boundary condition of friction type…
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
A Dirichlet-type problem is studied for an equation of even order with variable coefficients. A criterion for the uniqueness of a solution is given. The solution is built in the form of a Fourier series. When justifying the convergence of…
We derive effective wall-laws for Stokes systems with inhomogeneous boundary conditions in three dimensional bounded domains with curved rough boundaries. No-slip boundary condition is given on the locally periodic rough boundary parts with…