A posteriori error analysis and adaptivity for high-dimensional elliptic and parabolic boundary value problems

DOI10.1007/s00211-023-01350-2MaRDI QIDQ6044435

Fabian Merle, Andreas Prohl

Publication date: 19 May 2023

Published in: Numerische Mathematik (Search for Journal in Brave)

Mathematics Subject Classification ID

Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Complexity and performance of numerical algorithms (65Y20)

Cites Work

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• Axioms of adaptivity
• Tensor-sparsity of solutions to high-dimensional elliptic partial differential equations
• Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations
• Simulation of stopped diffusions
• Spatially adaptive sparse grids for high-dimensional data-driven problems
• Adaptive near-optimal rank tensor approximation for high-dimensional operator equations
• Solving Dirichlet problems numerically using the Feynman-Kac representation
• Weak approximation of killed diffusion using Euler schemes.
• Adaptive finite element methods with convergence rates
• The solving of boundary value problems by numerical integration of stochastic equations
• An adaptive time-stepping method based on a posteriori weak error analysis for large SDE systems
• HT-AWGM: a hierarchical Tucker-adaptive wavelet Galerkin method for high-dimensional elliptic problems
• On the threshold condition for Dörfler marking
• Stopped diffusion processes: boundary corrections and overshoot
• Approximation rates for the hierarchical tensor format in periodic Sobolev spaces
• Optimality of a standard adaptive finite element method
• A posteriori error estimates for finite element discretizations of the heat equation
• Adaptive low-rank methods for problems on Sobolev spaces with error control in L₂
• Optimality of an adaptive finite element method for the p-Laplacian equation
• Treatment of incompatible initial and boundary data for parabolic equations in higher dimension
• An Exit Probability Approach to Solving High Dimensional Dirichlet Problems
• Theory of adaptive finite element methods: An introduction
• Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
• Weak approximation of a diffusion process in a bounded domain
• The Simplest Random Walks for the Dirichlet Problem
• Euler schemes and half-space approximation for the simulation of diffusion in a domain
• Design and convergence analysis for an adaptive discretization of the heat equation
• Convergence of Adaptive Finite Element Methods
• Adaptive weak approximation of stochastic differential equations
• An adaptive finite element algorithm with reliable and efficient error control for linear parabolic problems
• A Convergent Adaptive Algorithm for Poisson’s Equation
• Singular value decomposition versus sparse grids: refined complexity estimates
• Sparse grids
• Numerical solution of parabolic equations in high dimensions
• Convergence Rates for Adaptive Weak Approximation of Stochastic Differential Equations
• Cubature, Approximation, and Isotropy in the Hypercube
• A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations
• Adaptive FEM with Optimal Convergence Rates for a Certain Class of Nonsymmetric and Possibly Nonlinear Problems
• Adaptive Monte Carlo Algorithms for Stopped Diffusion
• A convergent time–space adaptive dG(s) finite element method for parabolic problems motivated by equal error distribution

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