Summary:
The mathematical modeling of time-dependent processes in science and engineering leads to in general nonlinear evolution equations of first or second order. The highest spatial derivatives appearing can often be described by a monotone and coercive operator; semilinearities are then treated as a strongly continuous perturbation of the principle part. Relying upon the variational approach and the theory of monotone operators, the numerical solution of such evolution problems is studied with a focus on time discretization methods on equidistant as well as non-uniform meshes and their convergence. The results apply in particular to fluid flow problems.
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12065
Etienne Emmrich, Guy Vallet PDF
Project: B7
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Existence via time discretization for a class of doubly nonlinear operator-differential equations of Barenblatt-type |
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11045
Etienne Emmrich, David Siska PDF
Project: B7
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Full discretization of second-order nonlinear evolution equations: strong convergence and applications |
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11026
Etienne Emmrich, Mechthild Thalhammer PDF
Project: B7
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A class of integro-differential equations arising in nonlinear elastodynamics: Existence via time discretisation |
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11020
Etienne Emmrich, Aneta Wróblewska PDF
Project: B7
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Convergence of a full discretization of quasilinear parabolic equations in isotropic and anisotropic Orlicz spaces |
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10094
Etienne Emmrich, David Siska PDF
Full Discretization of the porous medium/fast diffusion equations based on its very weak formulation Project: B7
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Full Discretization of the porous medium/fast diffusion equations based on its very weak formulation |
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10034
Etienne Emmrich PDF
Discontinuous Galerkin in time approximation of monotone nonlinear evolution problems Published: BIT Numer. Math. 51, no. 3 (2011), 581-607 Notes: erschienen unter dem Titel "Time discretisation of monotone nonlinear evolution problems by the discontinuous Galerkin method" |
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10030
Etienne Emmrich, Mechthild Thalhammer PDF
Doubly nonlinear evolution equations of second order: Existence and fully discrete approximation Published: J. Differential Equations 251, no. 1 (2011), 82–118 |
