Related papers: A finite element method for high-contrast interfac…
We introduce a new method for studying stochastic homogenization of elliptic equations in nondivergence form. The main application is an algebraic error estimate, asserting that deviations from the homogenized limit are at most proportional…
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…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
We use the local orthogonal decomposition technique to derive a generalized finite element method for linear and semilinear parabolic equations with spatial multiscale diffusion coefficient. We consider nonsmooth initial data and a backward…
In this paper we propose, analyze, and test numerically a pressure-robust stabilized finite element for a linearized problem in incompressible fluid mechanics, namely, the steady Oseen equation with low viscosity. Stabilization terms are…
We study monotone P1 finite element methods on unstructured meshes for fully non-linear, degenerately parabolic Isaacs equations with isotropic diffusions arising from stochastic game theory and optimal control and show uniform convergence…
We propose a discontinuous least squares finite element method for solving the Helmholtz equation. The method is based on the L2 norm least squares functional with the weak imposition of the continuity across the interior faces as well as…
A homogenization approach is one of effective strategies to solve multiscale elliptic problems approximately. The finite element heterogeneous multiscale method (FEHMM) which is based on the finite element makes possible to simulate such…
We derive the optimal energy error estimate for multiscale finite element method with oversampling technique applying to elliptic system with rapidly oscillating periodic coefficients under the assumption that the coefficients are bounded…
We consider an elliptic linear-quadratic parameter estimation problem with a finite number of parameters. A novel a priori bound for the parameter error is proved and, based on this bound, an adaptive finite element method driven by an a…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
In this paper, we introduce the locally conservative enriched immersed finite element method (EIFEM) to tackle the elliptic problem with interface. The immersed finite element is useful for handling interface with mesh unfit with the…
We investigate $C^1$ finite element methods for one dimensional elliptic distributed optimal control problems with pointwise constraints on the derivative of the state formulated as fourth order variational inequalities for the state…
Analysis of an interface stabilised finite element method for the scalar advection-diffusion-reaction equation is presented. The method inherits attractive properties of both continuous and discontinuous Galerkin methods, namely the same…
In this paper we propose a finite element method for solving elliptic equations with the observational Dirichlet boundary data which may subject to random noises. The method is based on the weak formulation of Lagrangian multiplier. We show…
This article is concerned with the nonconforming finite element method for distributed elliptic optimal control problems with pointwise constraints on the control and gradient of the state variable. We reduce the minimization problem into a…
In this paper, we introduce a novel unfitted finite element method to solve the quad-curl interface problem. We adapt Nitsche's method for curlcurl-conforming elements and double the degrees of freedom on interface elements. To ensure…
In this paper we propose and analyze a new Multiscale Method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. For this purpose we construct a generalized finite element basis that spans…
Dealing with variational formulations of second order elliptic problems with discontinuous coefficients, we recall a single field minimization problem of an extended functional presented by Bevilacqua et al (1974), which we associate with…
We use a diffuse interface method for solving Poisson's equation with a Dirichlet condition on an embedded curved interface. The resulting diffuse interface problem is identified as a standard Dirichlet problem on approximating regular…