[图书][B] Mathematical theory of finite elements
LF Demkowicz - 2023 - SIAM
This monograph is based on my personal lecture notes for the graduate course on
Mathematical Theory of Finite Elements (EM394H) that I have been teaching at ICES (now …
Mathematical Theory of Finite Elements (EM394H) that I have been teaching at ICES (now …
[HTML][HTML] Adaptive Deep Fourier Residual method via overlapping domain decomposition
Abstract The Deep Fourier Residual (DFR) method is a specific type of variational physics-
informed neural network (VPINN). It provides a robust neural network-based solution to …
informed neural network (VPINN). It provides a robust neural network-based solution to …
Nonlocal half-ball vector operators on bounded domains: Poincaré inequality and its applications
This work contributes to nonlocal vector calculus as an indispensable mathematical tool for
the study of nonlocal models that arises in a variety of applications. We define the nonlocal …
the study of nonlocal models that arises in a variety of applications. We define the nonlocal …
Discretization of Linear Problems in Banach Spaces: Residual Minimization, Nonlinear Petrov--Galerkin, and Monotone Mixed Methods
I Muga, KG Van Der Zee - SIAM Journal on Numerical Analysis, 2020 - SIAM
This work presents a comprehensive discretization theory for abstract linear operator
equations in Banach spaces. The fundamental starting point of the theory is the idea of …
equations in Banach spaces. The fundamental starting point of the theory is the idea of …
Time-stepping DPG formulations for the heat equation
NV Roberts, S Henneking - Computers & Mathematics with Applications, 2021 - Elsevier
For a wide range of PDEs, the discontinuous Petrov–Galerkin (DPG) methodology of
Demkowicz and Gopalakrishnan provides discrete stability starting from a coarse mesh and …
Demkowicz and Gopalakrishnan provides discrete stability starting from a coarse mesh and …
Isogeometric analysis and Augmented Lagrangian Galerkin Least Squares Methods for residual minimization in dual norm
We explore how recent advances in Isogeometric analysis, Galerkin Least-Squares
methods, and Augmented Lagrangian techniques can be applied to solve nonstandard …
methods, and Augmented Lagrangian techniques can be applied to solve nonstandard …
A scalable hp-adaptive finite element software with applications in fiber optics
SKW Henneking - 2021 - repositories.lib.utexas.edu
In this dissertation, we present a scalable parallel version of hp3D—a finite element (FE)
software for analysis and discretization of complex three-dimensional multiphysics …
software for analysis and discretization of complex three-dimensional multiphysics …
A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems
Abstract We present a Petrov-Galerkin (PG) method for a class of nonlocal convection-
dominated diffusion problems. There are two main ingredients in our approach. First, we …
dominated diffusion problems. There are two main ingredients in our approach. First, we …
Error representation of the time-marching DPG scheme
In this article, we introduce an error representation function to perform adaptivity in time of
the recently developed time-marching Discontinuous Petrov–Galerkin (DPG) scheme. We …
the recently developed time-marching Discontinuous Petrov–Galerkin (DPG) scheme. We …
An anisotropic hp-adaptation framework for ultraweak discontinuous Petrov–Galerkin formulations
In this article, we present a three-dimensional anisotropic hp-mesh refinement strategy for
ultraweak discontinuous Petrov–Galerkin (DPG) formulations with optimal test functions. The …
ultraweak discontinuous Petrov–Galerkin (DPG) formulations with optimal test functions. The …