Numerical methods
Finite element method
Notes for "The Mathematical Theory of Finite Element Methods" by S. C. Brenner
- Chapter 0 (Password: 4wWz)
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% Math symbol commands
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\newcommand{\diff}{{\rm d}} % Symbol 'd' used in differentiation
\newcommand{\Diff}{{\rm D}} % Symbol 'D' used in differentiation
\newcommand{\pdiff}{\partial} % Partial derivative
\newcommand{DD}[2]{\frac{\diff}{\diff #2}\left( #1 \right)}
\newcommand{Dd}[2]{\frac{\diff #1}{\diff #2}}
\newcommand{PD}[2]{\frac{\pdiff}{\pdiff #2}\left( #1 \right)}
\newcommand{Pd}[2]{\frac{\pdiff #1}{\pdiff #2}}
\newcommand{\rme}{{\rm e}} % Exponential e
\newcommand{\rmi}{{\rm i}} % Imaginary unit i
\newcommand{\rmj}{{\rm j}} % Imaginary unit j
\newcommand{\vect}[1]{\boldsymbol{#1}} % Vector typeset in bold and italic
\newcommand{\phs}[1]{\dot{#1}} % Scalar phasor
\newcommand{\phsvect}[1]{\boldsymbol{\dot{#1}}} % Vector phasor
\newcommand{\normvect}{\vect{n}} % Normal vector: n
\newcommand{\dform}[1]{\overset{\rightharpoonup}{\boldsymbol{#1}}} % Vector for differential form
\newcommand{\cochain}[1]{\overset{\rightharpoonup}{#1}} % Vector for cochain
\newcommand{\bigabs}[1]{\bigg\lvert#1\bigg\rvert} % Absolute value (single big vertical bar)
\newcommand{\Abs}[1]{\big\lvert#1\big\rvert} % Absolute value (single big vertical bar)
\newcommand{\abs}[1]{\lvert#1\rvert} % Absolute value (single vertical bar)
\newcommand{\bignorm}[1]{\bigg\lVert#1\bigg\rVert} % Norm (double big vertical bar)
\newcommand{\Norm}[1]{\big\lVert#1\big\rVert} % Norm (double big vertical bar)
\newcommand{\norm}[1]{\lVert#1\rVert} % Norm (double vertical bar)
\newcommand{\ouset}[3]{\overset{#3}{\underset{#2}{#1}}} % over and under set
% Super/subscript for column index of a matrix, which is used in tensor analysis.
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% Example: $u(x)\restrict_{\Omega_0}$
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\DeclareMathOperator{\sgn}{sgn} % Sign function
\DeclareMathOperator{\erf}{erf} % Error function
\DeclareMathOperator{\Bd}{Bd} % Boundary of a set, used in topology
\DeclareMathOperator{\Int}{Int} % Interior of a set, used in topology
\DeclareMathOperator{\rank}{rank} % Rank of a matrix
\DeclareMathOperator{\divergence}{div} % Curl
\DeclareMathOperator{\curl}{curl} % Curl
\DeclareMathOperator{\grad}{grad} % Gradient
\DeclareMathOperator{\tr}{tr} % Trace
\DeclareMathOperator{\span}{span} % Span
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