Results 71 to 80 of about 625,960 (181)
Journal of Mathematics, 2017 In this paper, we investigate a mixed discontinuous Galerkin approximation of time dependent convection diffusion optimal control problem with control constraints based on the combination of a mixed finite element method for the elliptic part and a ...
Qingjin Xu, Zhaojie Zhou
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Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.ABSTRACT Due to the widespread usage of specialized piezoelectric actuators in various applications, accurate simulations have become key components of modern design processes. Although simulation tools for piezoelectric devices are widely available, nonlinear effects, which occur when exciting near resonance at elevated amplitudes, are often neglected
Jonas Hölscher +2 more
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Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.ABSTRACT Strain‐space reduced cubature techniques such as the Empirically Corrected Cluster Cubature (E3C) considerably reduce the integration effort incurred in computational homogenisation problems. In this work, we apply E3C in tandem with projection‐based model reduction techniques utilising both linear and quadratic approximation spaces.
Erik Faust, Dong Zhao, Lisa Scheunemann
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Rellich-type Discrete Compactness for Some Discontinuous Galerkin FEM [PDF]
We deduce discrete compactness of Rellich type for some discontinuous Galerkin finite element methods (DGFEM) including hybrid ones, under fairly general settings on the triangulations and the finite element spaces.
KIKUCHI, Fumio
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Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.ABSTRACT A potential–based, first–integral formulation of the Navier–Stokes equations is used as a platform for modelling solitary waves in gravity‐driven film flow, giving rise to a nonlinear partial differential equation in complex form. Its subsequent modal decomposition—leading to an infinite set of ordinary differential equations (ODEs), followed ...
Markus Scholle +2 more
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On fully discrete Galerkin approximations for the Cahn‐Hilliard equation
Mathematical Modelling and Analysis, 2004 Standard Galerkin approximations, using smooth splines to solutions of the nonlinear evolutionary Cahn‐Hilliard equation are analysed. The existence, uniqueness and convergence of the fully discrete Crank‐Nicolson scheme are discussed.
K. Omrani
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Global Existence for Stochastic Strongly Dissipative Zakharov Equations
Advances in Mathematical Physics, 2020 The stochastic strongly dissipative Zakharov equations with white noise are studied. On the basis of the time uniform a priori estimates, we prove the existence and uniqueness of solutions in energy spaces E1 and E2, by using the standard Galerkin ...
Xueqin Wang, Yadong Shang, Chunlin Lei
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Continuation of Periodic Solutions in Conservative Systems Leveraging the First Integral of Motion
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.ABSTRACT Dynamical systems are often analysed with respect to a system parameter, for which numerical continuation methods are typically used. In most cases, dissipative systems are considered. Here, the continuation of periodic solutions requires the existence of an explicit parameter that can be varied during the continuation process.
Julian Vogelei +2 more
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Shooting Methods for Boundary Value Problems of Fractional Differential Equations
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.ABSTRACT We consider two‐point boundary value problems of fractional differential equations (FDEs) including a Caputo derivative with a fractional order in the range (0,1) or (1,2). The numerical solution of a boundary value problem is investigated using shooting methods.
Roland Pulch, Abhishek Kumar Singh
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Derivation of an adjoint consistent discontinuous Galerkin discretization of the compressible Euler equations [PDF]
, 2006 Adjoint consistency - in addition to consistency - is the key requirement for discontinuous Galerkin (DG) discretizations to be of optimal order in L2 as well as measured in terms of target functionals.
Hartmann, Ralf
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