Partial Differential Equations
Explore equations and data; model equations; weak solutions and discretization. Concepts and connections are available independently of video coverage.
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PDE classification
Second-order principal terms distinguish elliptic, parabolic and hyperbolic behavior under appropriate assumptions.
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Boundary value problems
Boundary data restrict a differential equation's solution on the edge of its domain.
Partial differential equations
A PDE relates a multivariable unknown function to its partial derivatives.
Well-posedness
A well-posed problem has a solution, uniqueness and continuous dependence on data.
Energy estimates
Bounds on integrated solution quantities help establish stability and uniqueness.
Finite element method
Piecewise basis functions approximate weak formulations over a subdivided domain.
Knowledge connections
- Boundary value problems · Related · Map context
- Well-posedness · Related · Map context
- Partial differential equations · Prerequisite · Map context