Analysis of the Implicit Euler Local Uniform Grid Refinement Method
Copyright policy )Analysis of the Implicit Euler Local Uniform Grid Refinement Method
The authors investigate the behavior of numerical solutions with sharp moving transitions in space and time. An adaptive grid method is employed to refine the space grid locally and uniformly. The paper concentrates on stability and error analysis for implicit Euler time integration. It results in a refinement condition with a strategy for distributing spatial interpolation and discretization errors in such a way that the spatial accuracy obtained is comparable to the spatial accuracy on the finest grid if that grid would be used without any adaption.
Method of lines for initial value and initial-boundary value problems involving PDEs, sharp moving transitions, Error bounds for initial value and initial-boundary value problems involving PDEs, adaptive grid method, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, implicit Euler time integration, uniform grid refinement, Initial value problems for second-order parabolic equations, stability, error analysis
Method of lines for initial value and initial-boundary value problems involving PDEs, sharp moving transitions, Error bounds for initial value and initial-boundary value problems involving PDEs, adaptive grid method, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, implicit Euler time integration, uniform grid refinement, Initial value problems for second-order parabolic equations, stability, error analysis
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