Alexander Rieder
Alexander Rieder
We introduce a novel discretization technique for both elliptic and parabolic fractional diffusion problems based on double exponential quadrature formulas and the Riesz-Dunford functional calculus. Compared to related schemes, the new meth...
Goal-oriented adaptive finite element methods with optimal computational complexity [0.03%]
具有最优计算复杂性的基于目标的自适应有限元方法
Roland Becker,Gregor Gantner,Michael Innerberger et al.
Roland Becker et al.
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising...
On convergence rates of adaptive ensemble Kalman inversion for linear ill-posed problems [0.03%]
线性不适定问题下自适应经验卡尔曼逆演的收敛率分析
Fabian Parzer,Otmar Scherzer
Fabian Parzer
In this paper we discuss a deterministic form of ensemble Kalman inversion as a regularization method for linear inverse problems. By interpreting ensemble Kalman inversion as a low-rank approximation of Tikhonov regularization, we are able...
Exponential node clustering at singularities for rational approximation, quadrature, and PDEs [0.03%]
奇点处指数节点聚类的有理逼近、数值积分和偏微分方程问题
Lloyd N Trefethen,Yuji Nakatsukasa,J A C Weideman
Lloyd N Trefethen
Rational approximations of functions with singularities can converge at a root-exponential rate if the poles are exponentially clustered. We begin by reviewing this effect in minimax, least-squares, and AAA approximations on intervals and c...
Finite element approximation of the Laplace-Beltrami operator on a surface with boundary [0.03%]
带有边界曲面上Laplace-Beltrami算子的有限元逼近
Erik Burman,Peter Hansbo,Mats G Larson et al.
Erik Burman et al.
We develop a finite element method for the Laplace-Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced...
Convergence analysis of domain decomposition based time integrators for degenerate parabolic equations [0.03%]
基于区域分解的时间积分器对于退化抛物型方程的收敛性分析
Monika Eisenmann,Eskil Hansen
Monika Eisenmann
Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems. In this study, a rigours convergence analysis is given for such ...
Markus Faustmann,Jens Markus Melenk
Markus Faustmann
The local behavior of the lowest order boundary element method on quasi-uniform meshes for Symm's integral equation and the stabilized hyper-singular integral equation on polygonal/polyhedral Lipschitz domains is analyzed. We prove local a ...
Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients [0.03%]
带有QMC的循环嵌入：具有对数正态系数的椭圆PDE的分析
Ivan G Graham,Frances Y Kuo,Dirk Nuyens et al.
Ivan G Graham et al.
In a previous paper (Graham et al. in J Comput Phys 230:3668-3694, 2011), the authors proposed a new practical method for computing expected values of functionals of solutions for certain classes of elliptic partial differential equations w...
Convergence and adaptive discretization of the IRGNM Tikhonov and the IRGNM Ivanov method under a tangential cone condition in Banach space [0.03%]
Banach空间下IRGNM Tikhonov和IRGNM Ivanov方法的收敛性和自适应离散化（附切锥条件）
Barbara Kaltenbacher,Mario Luiz Previatti de Souza
Barbara Kaltenbacher
In this paper we consider the iteratively regularized Gauss-Newton method (IRGNM) in its classical Tikhonov version as well as two further-Ivanov type and Morozov type-versions. In these two alternative versions, regularization is achieved ...
Convergence of a linearly transformed particle method for aggregation equations [0.03%]
线性变换粒子方法在聚集方程中的收敛性
Martin Campos Pinto,José A Carrillo,Frédérique Charles et al.
Martin Campos Pinto et al.
We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in L1 and L∞ norms depending on the regularit...