2016
DOI: 10.5445/ir/1000056876
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A Parallel and Adaptive Space-Time Method for Maxwell's Equations

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Cited by 2 publications
(3 citation statements)
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“…In [8] (cf. also [19]), the space-time adaptive finite element discretization of the wave problem (1.1) is studied. For this, goal-oriented error estimation based on the dual weighted residual method [9] is used.…”
Section: Introductionmentioning
confidence: 99%
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“…In [8] (cf. also [19]), the space-time adaptive finite element discretization of the wave problem (1.1) is studied. For this, goal-oriented error estimation based on the dual weighted residual method [9] is used.…”
Section: Introductionmentioning
confidence: 99%
“…One reason for this might be the increasing complexity of the resulting linear and nonlinear algebraic systems if the approximations are built upon higher order piecewise polynomials in time and space; cf., e.g., [11,15,16,25,35]. Since recently, they have been applied for the numerical simulation of problems of practical interest; cf., e.g., [1,2,3,12,15,19,26,27,35]. Here we restrict ourselves to considering a family of continuous Galerkin-Petrov (cGP) methods in time and continuous Galerkin (cG) methods in space for second-order hyperbolic equations (cGP-cG method).…”
Section: Introductionmentioning
confidence: 99%
“…These auxiliary results then enable us to prove the desired optimal-order error estimates for u − u 0 τ,h and ∂ t u − u 1 τ,h . Space-time finite element methods with continuous and discontinuous discretizations of the time and space variables for parabolic and hyperbolic problems are well-known and have been studied carefully in the literature; cf., e.g., [1,2,7,8,10,12,14,15,[18][19][20][23][24][25][26][27][29][30][31]33,40,42] and the references therein. The space-time approaches of these works differ by the choices of the trial and, in particular, of the test spaces.…”
Section: Introductionmentioning
confidence: 99%