This class sets up a test that checks convergence rate for solution of the Poisson equation in 1D with Lagrange(2) basis functions. More...
Public Member Functions | |
| SimplePoisson1DTest (const Array< int > &nx) | |
| Construct the test object. | |
| std::string | name () const |
| Return a descriptive name for the test. | |
| Array< int > | pExpected () const |
| Return the expected order of accuracy for the solutions. | |
| Expr | exactSoln () const |
| Return an expression for the exact solution to the test problem. | |
| LinearProblem | prob (const Mesh &mesh) const |
| Return a LP for the specified mesh. | |
| Array< LPTestSpec > | specs () const |
| Specify which linear solvers are to be used. | |
Detailed Description
This class sets up a test that checks convergence rate for solution of the Poisson equation in 1D with Lagrange(2) basis functions.
The test problem is
![\[ u'' = -\frac{1}{4}\pi^2 \sin(\pi x/2) \]](form_211.png)
with boundary conditions
![\[ u(0)=1, \;\;\; u'(1)=0. \]](form_212.png)
The solution is 
.
Definition at line 47 of file LPTests1D.cpp.
Constructor & Destructor Documentation
| SimplePoisson1DTest::SimplePoisson1DTest | ( | const Array< int > & | nx | ) | [inline] |
Construct the test object.
The constructor calls the base class constructor with a list of mesh sizes to be used.
Definition at line 54 of file LPTests1D.cpp.
Member Function Documentation
| Expr SimplePoisson1DTest::exactSoln | ( | ) | const [inline, virtual] |
Return an expression for the exact solution to the test problem.
Implements Sundance::ForwardProblemTestBase.
Definition at line 68 of file LPTests1D.cpp.
References Sundance::ForwardProblemTestBase::coord().
| std::string SimplePoisson1DTest::name | ( | ) | const [inline, virtual] |
Return a descriptive name for the test.
Implements Sundance::ForwardProblemTestBase.
Definition at line 58 of file LPTests1D.cpp.
| Array<int> SimplePoisson1DTest::pExpected | ( | ) | const [inline, virtual] |
Return the expected order of accuracy for the solutions.
Because a problem might have multiple field variables, the expected orders of accuracy for the different variables are returned as an array.
Implements Sundance::ForwardProblemTestBase.
Definition at line 63 of file LPTests1D.cpp.
| LinearProblem SimplePoisson1DTest::prob | ( | const Mesh & | mesh | ) | const [inline, virtual] |
Return a LP for the specified mesh.
This function implements the prob() pure virtual function of class LPTestBase.
Implements Sundance::LPTestBase.
Definition at line 80 of file LPTests1D.cpp.
References Sundance::ForwardProblemTestBase::coord(), Sundance::LP1DTestBase::domain(), Sundance::gradient(), Sundance::LP1DTestBase::interior(), Sundance::LineDomain::left(), and Sundance::ForwardProblemTestBase::vecType().
| Array<LPTestSpec> SimplePoisson1DTest::specs | ( | ) | const [inline, virtual] |
Specify which linear solvers are to be used.
Reimplemented from Sundance::LPTestBase.
Definition at line 103 of file LPTests1D.cpp.