Consistent and stable meshfree Galerkin methods using the virtual element decomposition
Sign Up to like & getrecommendations! Published in 2017 at "International Journal for Numerical Methods in Engineering"
DOI: 10.1002/nme.5519
Abstract: Summary Over the past two decades, meshfree methods have undergone significant development as a numerical tool to solve partial differential equations (PDEs). In contrast to finite elements, the basis functions in meshfree methods are smooth… read more here.
Keywords: meshfree methods; basis functions; meshfree galerkin; galerkin methods ... See more keywords
Spectral analysis of matrices in Galerkin methods based on generalized B-splines with high smoothness
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DOI: 10.1007/s00211-016-0796-z
Abstract: We present a first step towards the spectral analysis of matrices arising from IgA Galerkin methods based on hyperbolic and trigonometric GB-splines. Second order differential problems with constant coefficients are considered and discretized by means… read more here.
Keywords: analysis matrices; analysis; spectral analysis; matrices galerkin ... See more keywords
Nonlinear Galerkin methods for a system of PDEs with Turing instabilities
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DOI: 10.1007/s10092-018-0245-8
Abstract: We address and discuss the application of nonlinear Galerkin methods for the model reduction and numerical solution of partial differential equations (PDE) with Turing instabilities in comparison with standard (linear) Galerkin methods. The model considered… read more here.
Keywords: time; nonlinear galerkin; turing instabilities; system pdes ... See more keywords
Stability of Nonlinear Convection–Diffusion–Reaction Systems in Discontinuous Galerkin Methods
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DOI: 10.1007/s10915-016-0256-z
Abstract: In this work we provide an extension of the classical von Neumann stability analysis for high-order accurate discontinuous Galerkin methods applied to generalized nonlinear convection–reaction–diffusion systems. We provide a partial linearization under which a sufficient… read more here.
Keywords: discontinuous galerkin; nonlinear convection; reaction; galerkin methods ... See more keywords
Discontinuous Galerkin Methods for Relativistic Vlasov–Maxwell System
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DOI: 10.1007/s10915-016-0332-4
Abstract: The relativistic Vlasov–Maxwell (RVM) system is a kinetic model that describes the dynamics of plasma when the charged particles move in the relativistic regime and their collisions are not important. In this paper, we formulate… read more here.
Keywords: system; vlasov maxwell; relativistic vlasov; discontinuous galerkin ... See more keywords
Discontinuous Galerkin Methods with Optimal $$L^2$$L2 Accuracy for One Dimensional Linear PDEs with High Order Spatial Derivatives
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DOI: 10.1007/s10915-018-0788-5
Abstract: In this paper, we formulate and analyze discontinuous Galerkin (DG) methods to solve several partial differential equations (PDEs) with high order spatial derivatives, including the heat equation, a third order wave equation, a fourth order… read more here.
Keywords: order; pdes high; order spatial; discontinuous galerkin ... See more keywords
High Order Still-Water and Moving-Water Equilibria Preserving Discontinuous Galerkin Methods for the Ripa Model
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DOI: 10.1007/s10915-020-01134-y
Abstract: Shallow water equations with horizontal temperature gradients, also known as the Ripa system, are used to model flows when the temperature fluctuations play an important role. These equations admit steady state solutions where the fluxes… read more here.
Keywords: water; discontinuous galerkin; well balanced; galerkin methods ... See more keywords
A unified study of continuous and discontinuous Galerkin methods
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DOI: 10.1007/s11425-017-9341-1
Abstract: A unified study is presented in this paper for the design and analysis of different finite element methods (FEMs), including conforming and nonconforming FEMs, mixed FEMs, hybrid FEMs, discontinuous Galerkin (DG) methods, hybrid discontinuous Galerkin… read more here.
Keywords: discontinuous galerkin; continuous discontinuous; unified study; galerkin methods ... See more keywords
Hybrid perturbation-Galerkin methods for structural reliability analysis
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DOI: 10.1016/j.probengmech.2017.05.001
Abstract: Abstract A major challenge in the reliability analysis of complex structures is to determine the response function or surface from which the limit state function can be established and hence the failure probability of the… read more here.
Keywords: reliability analysis; perturbation galerkin; perturbation; reliability ... See more keywords
Discontinuous Galerkin Methods for Solving a Frictional Contact Problem with Normal Compliance
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DOI: 10.1080/01630563.2018.1472609
Abstract: Abstract Several discontinuous Galerkin (DG) methods are introduced for solving a frictional contact problem with normal compliance, which is modeled as a quasi-variational inequality. Consistency, boundedness, and stability are established for the DG methods. Two… read more here.
Keywords: problem normal; discontinuous galerkin; contact problem; frictional contact ... See more keywords
Comparison of hybrid and standard discontinuous Galerkin methods in a mesh-optimisation setting
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DOI: 10.1080/10618562.2019.1588962
Abstract: This paper assesses the benefits of hybridization on the accuracy and efficiency of high-order discontinuous Galerkin (DG) discretizations. Two hybridized methods are considered in addition to DG: hybridized DG (HDG) and embedded DG (EDG). These… read more here.
Keywords: methods mesh; comparison hybrid; hybrid standard; discontinuous galerkin ... See more keywords