Code Reference¶

class manufacturedsol_heateqn_fenics.ProbFenicsNumpiHeat2d(symbsol, V, kappa=1)¶

This class takes a sympy expression as the manufactured solution \(u(t;x,y)\) to the nonstationary heat equation

\[u_t - \nabla \cdot (\kappa \nabla u) = f\]

completed with Dirichlet boundary conditions and an initial condition

and a FEM function space where the equation is approximated on.

Parameters:	symbsol – a symbolic expression with parameters t,x,y with internal names x[0], x[1], t V – FeNiCs functionspace on a 2D mesh kappa – diffusion coefficient: may be a constant value or a FEniCS expression in x[0] and x[1]. Defaults to 1

A = None¶

csr matrix representing the weak discrete \(-\nabla \cdot (\kappa \nabla )\) operator

M = None¶

csr matrix for the mass

comp_cur_error(uvec, tcur)¶

get the current error

Parameters:	uvec – vector of solution approximation tcur – current time
Returns:	the approximation error

currhs(tcur)¶

Compute the current source term

containing the actual source of the system plus the contribution from the Dirichlet boundary data

Parameters:	tcur – current time
Returns:	Vector of the current rhs

cursolprjtd(tcur)¶

Get the current solution projected onto the FEM space

Parameters:	tcur – current time
Returns:	vector of the current projected solution

expand_vec_to_fun(uvec)¶

expand uvec to the dolfin function representation

Parameters:	uvec – vector of a current solution approximation
Returns:	FEniCS function containing the values of uvec and the Dirichlet data

manufacturedsol_heateqn_fenics.test_impeul_int()¶

Example for the test of convergence of Implicit Euler

manufacturedsol_heateqn_fenics.tran_heat_eq2d(omega=1)¶

An example time varying 2D manufactured solution

Parameters:	omega – Parameter for the frequency. Defaults to 1
Returns:	A symbolic expression of a scalar function depending on the space variables x (internal name is x[0]) and y (internal name is x[1]) and the time variable t