Related papers: Robust Localization of the Best Error with Finite …
We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for nonlinear elliptic second-order equations of monotone type. The adaptive algorithm is based on residual-type a posteriori error estimators and…
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…
We devise a generalization of tree approximation that generates conforming meshes, i.e., meshes with a particular structure like edge-to-edge triangulations. A key feature of this generalization is that the choices of the cells to be…
This work develops a distributed optimization strategy with guaranteed exact convergence for a broad class of left-stochastic combination policies. The resulting exact diffusion strategy is shown in Part II to have a wider stability range…
In the first part of this paper, we establish a conditional optimality result for an adaptive mixed finite element method for the stationary Stokes problem discretized by the standard Taylor-Hood elements, under the assumption of the…
We prove an abstract convergence result for a family of dual-mesh based quadrature rules on tensor products of simplical meshes. In the context of the multilinear tensor-product finite element discretization of reaction-drift-diffusion…
We attempt to answer the question what data brings adaptive diffusion algorithms converging to true parameters. The discussion begins with the diffusion recursive least squares (RLS). When unknown parameters are scalar, the necessary and…
In this work we derive a posteriori error estimates for the convection-diffusion-reaction equation coupled with the Darcy-Forchheimer problem by a nonlinear external source depending on the concentration of the fluid. We introduce the…
In this work, we develop an adaptive nonconforming finite element algorithm for the numerical approximation of phase-field parameterized topology optimization governed by the Stokes system. We employ the conforming linear finite element…
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…
Adaptive networks are well-suited to perform decentralized information processing and optimization tasks and to model various types of self-organized and complex behavior encountered in nature. Adaptive networks consist of a collection of…
We consider a singularly perturbed reaction diffusion problem as a first order two-by-two system. Using piecewise discontinuous polynomials for the first component and $H_{div}$-conforming elements for the second component we provide a…
This paper investigates the problem of distributed stochastic approximation in multi-agent systems. The algorithm under study consists of two steps: a local stochastic approximation step and a diffusion step which drives the network to a…
We study finite element approximations of second-order elliptic problems with measure-valued right-hand sides supported on lower-dimensional sets. The exact solution generally lacks $H^1$-regularity due to the source singularity, which…
We present and analyse an implicit-explicit timestepping procedure with finite element spatial approximation for a semilinear reaction-diffusion systems on evolving domains arising from biological models, such as Schnakenberg's (1979). We…
In this paper, optimal convergence for an adaptive finite element algorithm for elastoplasticity is considered. To this end, the proposed adaptive algorithm is established within the abstract framework of the axioms of adaptivity [Comput.…
In this paper, we are interested in a general equation that has finite speed of propagation compatible with Einstein's theory of special relativity. This equation without external force fields has been derived recently by means of optimal…
In this paper, we study a parabolic reaction diffusion system with constraints that model biofilm growth. Within a unified framework encompassing multiple numerical schemes, we derive the first general convergence rates for approximating…
We prove precise rates of convergence for monotone approximation schemes of fractional and nonlocal Hamilton-Jacobi-Bellman (HJB) equations. We consider diffusion corrected difference-quadrature schemes from the literature and new…
A space-time interface-fitted approximation of an inverse source problem for the advection-diffusion equation with moving subdomains is investigated. The problem is reformulated as an optimization problem using Tikhonov regularization. A…