A weak formulation multiplies a differential equation by a test function, integrates, and uses integration by parts to move derivatives away from the unknown function. Natural boundary conditions appear in the resulting boundary terms.
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- Coercive bilinear form
- Coercive variable-coefficient Dirichlet form
- Coercive weak formulation of a coupled Dirichlet-Neumann system
- Divergence-form elliptic operator
- Elliptic boundary value problem
- Entropy flux for a scalar conservation law
- Finite element method
- Finite element solution of the one-dimensional Poisson equation
- Lax-Milgram theorem
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- Petrov-Galerkin method
- Poisson equation on a disk with angular forcing
- Variational problem
- Weak Robin problem for a uniformly elliptic operator
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