Eighty years of the finite element method: Birth, evolution, and future
This document presents comprehensive historical accounts on the developments of finite
element methods (FEM) since 1941, with a specific emphasis on developments related to …
element methods (FEM) since 1941, with a specific emphasis on developments related to …
Review of output-based error estimation and mesh adaptation in computational fluid dynamics
KJ Fidkowski, DL Darmofal - AIAA journal, 2011 - arc.aiaa.org
Error estimation and control are critical ingredients for improving the reliability of
computational simulations. Adjoint-based techniques can be used to both estimate the error …
computational simulations. Adjoint-based techniques can be used to both estimate the error …
[图书][B] Computing with hp-adaptive finite elements: volume 1 one and two dimensional elliptic and Maxwell problems
L Demkowicz - 2006 - taylorfrancis.com
Offering the only existing finite element (FE) codes for Maxwell equations that support hp
refinements on irregular meshes, Computing with hp-ADAPTIVE FINITE ELEMENTS …
refinements on irregular meshes, Computing with hp-ADAPTIVE FINITE ELEMENTS …
Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality
We give an overview of recent developments concerning the use of adjoint methods in two
areas: the a posteriori error analysis of finite element methods for the numerical solution of …
areas: the a posteriori error analysis of finite element methods for the numerical solution of …
On residual-based a posteriori error estimation in hp-FEM
JM Melenk, BI Wohlmuth - Advances in Computational Mathematics, 2001 - Springer
A family η α, α∈[0, 1], of residual-based error indicators for the hp-version of the finite
element method is presented and analyzed. Upper and lower bounds for the error indicators …
element method is presented and analyzed. Upper and lower bounds for the error indicators …
A note on the design of hp-adaptive finite element methods for elliptic partial differential equations
We introduce an hp-adaptive finite element algorithm based on a combination of reliable
and efficient residual error indicators and a new hp-extension control technique which …
and efficient residual error indicators and a new hp-extension control technique which …
hp-Adaptive Discontinuous Galerkin Finite Element Methods for First-Order Hyperbolic Problems
We consider the {a posteriori} error analysis of hp-discontinuous Galerkin finite element
approximations to first-order hyperbolic problems. In particular, we discuss the question of …
approximations to first-order hyperbolic problems. In particular, we discuss the question of …
A Comparison of hp-Adaptive Strategies for Elliptic Partial Differential Equations
WF Mitchell, MA McClain - ACM Transactions on Mathematical Software …, 2014 - dl.acm.org
The hp version of the finite element method (hp-FEM) combined with adaptive mesh
refinement is a particularly efficient method for solving PDEs because it can achieve an …
refinement is a particularly efficient method for solving PDEs because it can achieve an …
Efficient nonlinear solvers for nodal high-order finite elements in 3D
J Brown - Journal of Scientific Computing, 2010 - Springer
Conventional high-order finite element methods are rarely used for industrial problems
because the Jacobian rapidly loses sparsity as the order is increased, leading to …
because the Jacobian rapidly loses sparsity as the order is increased, leading to …
A higher degree immersed finite element method based on a Cauchy extension for elliptic interface problems
This article develops and analyzes ap th degree immersed finite element (IFE) method for
solving the elliptic interface problems with meshes independent of the coefficient …
solving the elliptic interface problems with meshes independent of the coefficient …