Related papers: Stabilised finite element methods for ill-posed pr…
In this thesis, we investigate a novel local projection based stabilized conforming virtual element method for the generalized Oseen problem using equal-order element pairs on general polygonal meshes. To ensure the stability, particularly…
A stabilizing/penalty term is often used in finite element methods with discontinuous approximations to enforce connection of discontinuous functions across element boundaries. Removing stabilizers from discontinuous finite element methods…
In this paper, we consider the unique continuation problem for the Schr\"odinger equations. We prove a H\"older type conditional stability estimate and build up a parameterized stabilized finite element scheme adaptive to the \textit{a…
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…
In this paper, the problem of non-fragile finite-time stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli…
We discretize the Lagrange multiplier formulation of the obstacle problem by mixed and stabilized finite element methods. A priori and a posteriori error estimates are derived and numerically verified.
The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the…
This work presents and analyzes space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of parabolic optimal control problems. Using Babu\v{s}ka's theorem, we show well-posedness of…
We study numerical methods for solving a system of quasilinear stochastic partial differential equations known as the stochastic Landau-Lifshitz-Bloch (LLB) equation on a bounded domain in $\mathbb R^d$ for $d=1,2$. Our main results are…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in three-dimensional space. The method employs generalized Taylor-Hood finite element pairs on tetrahedral bulk mesh to discretize the…
We define a new finite element method for a steady state elliptic problem with discontinuous diffusion coefficients where the meshes are not aligned with the interface. We prove optimal error estimates in the $L^2$ norm and $H^1$ weighted…
In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well-known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the…
The paper [Shi19] uses the Craig-Wayne-Bourgain method to construct solutions of an elliptic problem involving parameters. The results of [Shi19] include regularity assumptions on the perturbation and involve excluding parameters. The paper…
We consider a stabilized finite element method for the Darcy problem on a surface based on the Masud-Hughes formulation. A special feature of the method is that the tangential condition of the velocity field is weakly enforced through the…
In this paper, we consider a nonlinear beam equation with the p-biharmonic operator, where $1 < p < \infty$. Using a change of variable, we transform the problem into a system of differential equations and prove the existence, uniqueness…
In this note we study the convergence of monotone P1 finite element methods on unstructured meshes for fully non-linear Hamilton-Jacobi-Bellman equations arising from stochastic optimal control problems with possibly degenerate, isotropic…
The implementation of the finite element method for linear elliptic equations requires to assemble the stiffness matrix and the load vector. In general, the entries of this matrix-vector system are not known explicitly but need to be…
This paper introduces a new variational formulation for Dirichlet boundary control problem of elliptic partial differential equations, based on observations that the state and adjoint state are related through the control on the boundary of…
In this study a stabilized finite element method for solving advection-diffusion-reaction equation with spatially variable coefficients has been carried out. Here subgrid scale approach along with algebraic approximation to the sub-scales…