The phase field method for geometric moving interfaces and their numerical approximations
This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …
surface evolution and related geometric nonlinear partial differential equations (PDEs) …
[BOOK][B] The mathematical theory of finite element methods
SC Brenner - 2008 - Springer
Untitled Page 1 Page 2 15 Texts in Applied Mathematics Editors JE Marsden L. Sirovich SS
Antman Advisors G. Iooss P. Holmes D. Barkley M. Dellnitz P. Newton Page 3 Texts in Applied …
Antman Advisors G. Iooss P. Holmes D. Barkley M. Dellnitz P. Newton Page 3 Texts in Applied …
[BOOK][B] Robust numerical methods for singularly perturbed differential equations
HG Roos - 2008 - Springer
The analysis of singular perturbed differential equations began early in the twentieth
century, when approximate solutions were constructed from asymptotic expansions …
century, when approximate solutions were constructed from asymptotic expansions …
A review of numerical methods for nonlinear partial differential equations
E Tadmor - Bulletin of the American Mathematical Society, 2012 - ams.org
Numerical methods were first put into use as an effective tool for solving partial differential
equations (PDEs) by John von Neumann in the mid-1940s. In a 1949 letter von Neumann …
equations (PDEs) by John von Neumann in the mid-1940s. In a 1949 letter von Neumann …
[BOOK][B] Finite elements II
A Ern, JL Guermond - 2021 - Springer
The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …
impact of computer technology, the growing importance of computer modelling and the …
[BOOK][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 …
[BOOK][B] Lecture notes in computational science and engineering
TJ Barth, M Griebel, DE Keyes, RM Nieminen, D Roose… - 2005 - Springer
The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …
models based on differential equations. Initially, the FEniCS Project consisted of two …
Quasi-optimal convergence rate for an adaptive finite element method
JM Cascon, C Kreuzer, RH Nochetto… - SIAM Journal on Numerical …, 2008 - SIAM
We analyze the simplest and most standard adaptive finite element method (AFEM), with
any polynomial degree, for general second order linear, symmetric elliptic operators. As is …
any polynomial degree, for general second order linear, symmetric elliptic operators. As is …
Optimality of a standard adaptive finite element method
R Stevenson - Foundations of Computational Mathematics, 2007 - Springer
In this paper an adaptive finite element method is constructed for solving elliptic equations
that has optimal computational complexity. Whenever, for some s> 0, the solution can be …
that has optimal computational complexity. Whenever, for some s> 0, the solution can be …
Approximation of high-dimensional parametric PDEs
A Cohen, R DeVore - Acta Numerica, 2015 - cambridge.org
Parametrized families of PDEs arise in various contexts such as inverse problems, control
and optimization, risk assessment, and uncertainty quantification. In most of these …
and optimization, risk assessment, and uncertainty quantification. In most of these …