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Bernardi, Christine; Süli, Endre

Time and space adaptivity for the second-order wave equation. (English) Zbl 1070.65083

Math. Models Methods Appl. Sci. 15, No. 2, 199-225 (2005).
The paper deals with an a posteriori error analysis of fully discrete approximations to the initial-boundary value problem for the wave equation \(u_{tt} - \Delta u = 0\) in a bounded connected open domain in \(\mathbb{R}^d\), \(d \leq 3\). The authors show that the adaptation of the time steps can be combined with the spatial mesh adaptivity in an optimal way.
Reviewer: Emil Minchev (Tokyo)

Cited in 1 Review
Cited in 27 Documents

MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L05 Wave equation

Keywords:

wave equation; backward Euler scheme; finite elements
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References:

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