How to solve the stochastic partial differential equation that gives a\n Mat 'ern random field using the finite element method

2018/03/10 by Haakon Bakka, Bakka, Haakon
Computer Science · Decision Sciences · Environmental Science · #Advanced Multi-Objective Optimization Algorithms #Computation (stat.CO) #FOS: Computer and information sciences #Probabilistic and Robust Engineering Design #Soil Geostatistics and Mapping

paper · pdf · doi:10.48550/arxiv.1803.03765

openalex publication_date 2018/03/10 · openalex created_date 2022/08/07 · openalex updated_date 2026/07/28

Abstract

This tutorial teaches parts of the finite element method (FEM), and solves a\nstochastic partial differential equation (SPDE). The contents herein are\nconsidered "known" in the numerics literature, but for statisticians it is very\ndifficult to find a resource for learning these ideas in a timely manner\n(without doing a year's worth of courses in numerics). The goal of this\ntutorial is to be pedagogical and explain the computations/theory to a\nstatistician. This is not a practical tutorial, there is little computer code,\nand no data analysis.\n

Related

• Solving Stochastic PDEs Using FEniCS and UQtk
• Stochastic PDE representation of random fields for large-scale Gaussian process regression and statistical finite element analysis
• Domain Decomposition of Stochastic PDEs: Development of Probabilistic Wirebasket-based Two-level Preconditioners
• A gentle introduction to SPDEs: the random field approach
• Stochastic Numerical Methods: An Introduction for Students and Scientists