Parabolic Partial Differential Equations
Evolution problems arise in all areas of science and engineering applications. Many evolution processes are dissipative in nature and can be modeled by parabolic partial differential equations (PDEs). Parabolic PDEs possess mathematical properties that have had a profound impact on the design of numerical methods for their approximate solution. Most notably, the cylindrical nature of the space–time domain has naturally led to discretizations by finite element methods in space and finite difference methods in time. As a rule, such separated discretizations lead to marching schemes, i.e., methods for which the approximate solution is obtained one time level at a time, requiring the solution of an elliptic PDE at each time level.
KeywordsElement Space Velocity Boundary Condition Parabolic Partial Differential Equation Optimal Error Estimate Parabolic PDEs
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