Standard heat resp. diffusion equation for an evolving or stationary surface problem. More...

#include <memory>
#include "esfem_fwd.h"

Include dependency graph for secOrd_op_linearHeat.h:

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Namespaces
	Esfem
	The evolving surface finite element method.

	Esfem::SecOrd_op
	Parabolic and elliptic second order operators.

Detailed Description

Standard heat resp. diffusion equation for an evolving or stationary surface problem.

Revision history

 Revised by Christian Power dd.mm.yyyy
 Originally written by Christian Power
      (power22c@gmail.com) 28. Januar 2016

Provides a class that performs the standard Dziuk Elliott evolving surface finite element discretization with implicit euler time discretization.

Search for $u\colon \surface \to \R$ for

$\begin{equation*} \matd u + u \diver(v) - \laplaceBeltrami u = f \end{equation*}$

Search for $\nodalValue{u}\colon I \to \R^N$ for

$\begin{equation*} \dell_t \parentheses[\big]{M(t) \nodalValue{u} } + A(t) \nodalValue{u} = M(t)\nodalValue{Pf}, \end{equation*}$

where $\nodalValue{Pf}$ are the nodal values of the $ L^2 $ -projection of $ f $ .

Given $\nodalValue{u}^n$ solve for $\nodalValue{u}^{n+1}$

$\begin{equation*} (M\nodalValue{u})^{n+1} + \tau (A \nodalValue{u})^{n+1} = (M \nodalValue{w})^n + \tau (M \nodalValue{Pf})^{n+1} \end{equation*}$

This programm implements a basic expression calculator.
Input from cin; output to cout.  The grammar for input is: etc.