Related papers: Convergence of the adaptive finite element discret…
We introduce an adaptive finite element scheme for the efficient approximation of a (large) collection of eigenpairs of selfadjoint elliptic operators in which the adaptive refinement is driven by the solution of a single source problem --…
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…
Optimization problems with $L^1$-control cost functional subject to an elliptic partial differential equation (PDE) are considered. However, different from the finite dimensional $l^1$-regularization optimization, the resulting discretized…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…
For the parallel computation of partial differential equations, one key is the grid partitioning. It requires that each process owns the same amount of computations, and also, the partitioning quality should be proper to reduce the…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…
In this paper we prove the optimal convergence of a standard adaptive scheme based on edge finite elements for the approximation of the solutions of the eigenvalue problem associated with Maxwell's equations. The proof uses the known…
Semi-infinite programming can be used to model a large variety of complex optimization problems. The simple description of such problems comes at a price: semi-infinite problems are often harder to solve than finite nonlinear problems. In…
This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a…
In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…
In two and three dimensions, we analyze a finite element method to approximate the solutions of an eigenvalue problem arising from neutron transport. We derive the eigenvalue problem of interest, which results to be non-symmetric. Under a…
In this paper, we give a numerical analysis for the transmission eigenvalue problem by the finite element method. A type of multilevel correction method is proposed to solve the transmission eigenvalue problem. The multilevel correction…
Finite element approximation to a decoupled formulation for the quad--curl problem is studied in this paper. The difficulty of constructing elements with certain conformity to the quad--curl problems has been greatly reduced. For convex…
Building on the successes of local kernel methods for approximating the solutions to partial differential equations (PDE) and the evaluation of definite integrals (quadrature/cubature), a local estimate of the error in such approximations…
This paper is concerned with the design and analysis of a fully adaptive eigenvalue solver for linear symmetric operators. After transforming the original problem into an equivalent one formulated on $\ell_2$, the space of square summable…
We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…
This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard space-time finite element spaces on a…
We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…