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         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2145f2b136dcc8119767623101fc74d5f/florianbienert",         
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         "label" : "Experimental analysis on CPA-free thin-disk multipass amplifiers operated in a helium-rich atmosphere",
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         "journal": "Opt. Express","publisher":"Optica Publishing Group",
         "year": "2022", 
         "url": "https://opg.optica.org/oe/abstract.cfm?URI=oe-30-21-38027", 
         
         "author": [ 
            "Florian Bienert","André Loescher","Christoph Röcker","Thomas Graf","Marwan Abdou Ahmed"
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            	{"first" : "Florian",	"last" : "Bienert"},
            	{"first" : "André",	"last" : "Loescher"},
            	{"first" : "Christoph",	"last" : "Röcker"},
            	{"first" : "Thomas",	"last" : "Graf"},
            	{"first" : "Marwan Abdou",	"last" : "Ahmed"}
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         "volume": "30","number": "21","pages": "38027--38042","abstract": "We present an experimental investigation on the benefits of helium as an atmospheric gas in CPA-free thin-disk multipass amplifiers (TDMPAs) for the amplification to average powers exceeding 1 kW and pulse peak powers reaching 5 GW. Both the performance of the amplifier and the properties of the amplified sub-400 fs laser pulses centred at a wavelength of 1030 nm are compared for different helium concentrations in air, outlining and quantifying the benefits of a helium-rich atmosphere. The amplification of 100 &\\#x00B5;J pulses in an atmosphere with 60&\\#x0025; helium instead of air led to a maximum increase in efficiency from 24&\\#x0025; to 29&\\#x0025;. This translated into an increase of average output power and pulse energy of 34 W (i.e &\\#x002B;19&\\#x0025;) and 0.34 mJ (i.e. &\\#x002B;19&\\#x0025;) respectively. At the same time an improvement of the beam quality from M2 &\\#x003D; 1.18 to M2 &\\#x003D; 1.14 was achieved. For the amplification of 10 &\\#x00B5;J pulses to over 1&\\#x2005;kW of average power an atmosphere with 33&\\#x0025; helium led to an improved beam pointing stability by a factor of 2. Moreover, the beam propagation factor M2 improved by 0.1, and the power stability improved by approximately 10&\\#x0025;.",
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         "author": [ 
            "Florian Bienert","André Loescher","Christoph Röcker","Thomas Graf","Marwan Abdou Ahmed"
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            	{"first" : "Florian",	"last" : "Bienert"},
            	{"first" : "André",	"last" : "Loescher"},
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         "volume": "30","number": "21","pages": "38027--38042","abstract": "We present an experimental investigation on the benefits of helium as an atmospheric gas in CPA-free thin-disk multipass amplifiers (TDMPAs) for the amplification to average powers exceeding 1 kW and pulse peak powers reaching 5 GW. Both the performance of the amplifier and the properties of the amplified sub-400 fs laser pulses centred at a wavelength of 1030 nm are compared for different helium concentrations in air, outlining and quantifying the benefits of a helium-rich atmosphere. The amplification of 100 &\\#x00B5;J pulses in an atmosphere with 60&\\#x0025; helium instead of air led to a maximum increase in efficiency from 24&\\#x0025; to 29&\\#x0025;. This translated into an increase of average output power and pulse energy of 34 W (i.e &\\#x002B;19&\\#x0025;) and 0.34 mJ (i.e. &\\#x002B;19&\\#x0025;) respectively. At the same time an improvement of the beam quality from M2 &\\#x003D; 1.18 to M2 &\\#x003D; 1.14 was achieved. For the amplification of 10 &\\#x00B5;J pulses to over 1&\\#x2005;kW of average power an atmosphere with 33&\\#x0025; helium led to an improved beam pointing stability by a factor of 2. Moreover, the beam propagation factor M2 improved by 0.1, and the power stability improved by approximately 10&\\#x0025;.",
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         "journal": "Chemische Berichte",
         "year": "1991", 
         "url": "", 
         
         "author": [ 
            "Andreas Schulz","Wolfgang. Kaim"
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            	{"first" : "Andreas",	"last" : "Schulz"},
            	{"first" : "Wolfgang.",	"last" : "Kaim"}
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         "volume": "124","number": "1","pages": "129--139","abstract": "The outstanding position of the 1,4-isomer, quinoxaline, among the diazanaphthalenes is confirmed by comparing LUMO energies from HMO perturbation calcns.  Diquaternary salts of quinoxaline, 2,3- and 6,7-dimethylquinoxaline and 2,3,6,7-tetramethylquinoxaline were isolated and characterized as compds. which are sensitive to redn. and hydrolysis.  Cyclic voltammetry of the two-step redox systems of the Weitz type showed two reversible one-electron redns. with an extraordinarily stable radical-cation intermediate (log Kc \\textgreater12).  The redox potentials are less neg. than those of the 4,4'-bipyridinium systems but also less pos. than those of N,N'-dialkylphenazinium compds.  The radical-cation intermediates, which include a TCNQ.bul.- salt, are characterized by ESR and by absorption spectroscopy in comparison to the resp. dications. [on SciFinder(R)]",
         "issn" : "0009-2940",
         
         "bibtexKey": "Schulz.1991"

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         "author": [ 
            "Hynek Kovar\\'ık","Semjon Vugalter","Timo Weidl"
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         "volume": "275","number": "3","pages": "827--838","abstract": "A logarithmic type Lieb-Thirring inequality fort wo-dimensional Schrödinger operators is established. The result is applied to prove spectral estimates on trapped modes in quantum layers.",
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         "mrreviewer" : "Pavel V. Exner",
         
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         "volume": "275","number": "3","pages": "827--838","abstract": "A logarithmic type Lieb-Thirring inequality for two-dimensional Schrödinger operators is established. The result is applied to prove spectral estimates on trapped modes in quantum layers.",
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            "World Scientific Publishing"
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         "pages": "110-129","abstract": "We summarize some of the improvements on Lieb-Thirring estimates during the past decade. In particular, we discuss logarithmic Lieb-Thirring estimates and Berezin-Li-Yau bounds with second order remainder terms.",
         "language" : "English",
         
         "doi" : "10.1142/9789814350365_0009",
         
         "bibtexKey": "weidl2011semiclassical"

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         "pages": "110-129","abstract": "We summarize some of the improvements on Lieb-Thirring estimates during the past decade. In particular, we discuss logarithmic Lieb-Thirring estimates and Berezin-Li-Yau bounds with second order remainder terms.",
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         "author": [ 
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            	{"first" : "Leander",	"last" : "Geisinger"},
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         "author": [ 
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         "volume": "23","number": "6","pages": "615-641","abstract": "We consider the Dirichlet Laplace operator on open, quasi-bounded domains of infinite volume. For such domains semiclassical spectral estimates based on the phase-space volume - and therefore on the volume of the domain - must fail. Here we present a method how one can nevertheless prove uniform bounds on eigenvalues and eigenvalue means which are sharp in the semiclassical limit. We give examples in horn-shaped regions and so-called spiny urchins. Some results are extended to Schrödinger operators defined on quasi-bounded domains with Dirichlet boundary conditions.",
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         "author": [ 
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            	{"first" : "Leander",	"last" : "Geisinger"},
            	{"first" : "Timo",	"last" : "Weidl"}
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         "bibtexKey": "geisinger2011sharp"

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         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2480eb8d27436d1813f64a75501305a78/mathematik",         
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         "label" : "Spectral estimates for the Heisenberg Laplacian on cylinders.",
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         "journal": "Functional Analysis and Operator Theory for Quantum Physics, EMS Series of Congress Reports, J. Dittrich, et al. (eds.)",
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         "author": [ 
            "Hynek Kovarik","Bartosch Ruszkowski","Timo Weidl"
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         "authors": [
         	
            	{"first" : "Hynek",	"last" : "Kovarik"},
            	{"first" : "Bartosch",	"last" : "Ruszkowski"},
            	{"first" : "Timo",	"last" : "Weidl"}
         ],
         "pages": "433-446","abstract": "\"In this paper the authors consider the Heisenberg Laplacian in a domain Ω⊂ℝ3 with Dirichlet boundary conditions, formally given by\r\nA(Ω)=−X21−X22,\r\nwhere\r\nX1=∂x1+x22∂x3,X2=∂x2−x12∂x3.\r\n   The main result of the paper is a uniform upper bound with remainder of the quantity\r\nTr(A(Ω)−λ)−,\r\nthat is, the sum of all eigenvalues of A(Ω) smaller than λ, counted according to their multiplicities. \r\n   Previous and optimal results on the leading term were known from [A. M. Hansson and A. Laptev, in Groups and analysis, 100\u2013115, London Math. Soc. Lecture Note Ser., 354, Cambridge Univ. Press, Cambridge, 2008; MR2528463], and improved estimates were obtained in [H. Kovařík and T. Weidl, Proc. Roy. Soc. Edinburgh Sect. A 145 (2015), no. 1, 145\u2013160; MR3304579], where it was proved that for any bounded domain Ω⊂ℝ3 there exists a constant C(Ω)>0 such that\r\nTr(A(Ω)−λ)−≤max0,|Ω|96λ3−C(Ω)λ2.\r\n\r\n   In this paper, the authors improve the above estimate for cylindrical domains of the form Ω=ω×(a,b), where ω⊂ℝ2 is an open, simply connected, bounded set. Their main result (Theorem 2.3) is an estimate of the form\r\nTr(A(Ω)−λ)−≤max0,|Ω|96λ3−D(Ω)λ(2c+5)/(c+2),(1)\r\nwhere c is the best Hardy constant for ω, and the constant D(Ω) depends explicitly on the cylindrical domain Ω. Notice that the correction term in (1) is of order larger than λ2. \r\n   For cylinders Ω=ω×(a,b) with convex cross-section ω, the above estimate reads:\r\nTr(A(Ω)−λ)−≤max0,|Ω|96λ3−λ2+1/427⋅35/2|Ω|R(ω)3/2,\r\nwhere R(ω) is the Euclidean in-radius of ω. \r\n   The main techniques employed are the relation of A(Ω) with the magnetic Laplacian (with constant magnetic field) and Hardy inequalities.\"",
         "bibtexKey": "kovarik2017spectral"

      }
,
      {
         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/20e1f49c7962599f662210ebaff44b50b/mathematik",         
         "tags" : [
            "iadm","from:elkepeter","asymptotics","Hänel","Weidl","Spectral"
         ],
         
         "intraHash" : "0e1f49c7962599f662210ebaff44b50b",
         "interHash" : "0e936fa8a9fa8b397cdce8f023e68e69",
         "label" : "Spectral asymptotics for the Dirichlet Laplacian with a Neumann window via a Birman-Schwinger analysis of the Dirichlet-to-Neumann operator.",
         "user" : "mathematik",
         "description" : "",
         "date" : "2021-10-13 13:52:26",
         "changeDate" : "2021-10-13 11:52:26",
         "count" : 3,
         "pub-type": "article",
         "journal": "Functional Analysis and Operator Theory for Quantum Physics, EMS Series of Congress Reports, J. Dittrich, et al. (eds.)",
         "year": "2017", 
         "url": "", 
         
         "author": [ 
            "André Hänel","Timo Weidl"
         ],
         "authors": [
         	
            	{"first" : "André",	"last" : "Hänel"},
            	{"first" : "Timo",	"last" : "Weidl"}
         ],
         "pages": "315 - 352","abstract": "\"In the present article we will give a new proof of the ground state asymptotics of the Dirichlet Laplacian with a Neumann window acting on functions which are defined on a two-dimensional infinite strip or a three-dimensional infinite layer. The proof is based on the analysis of the corresponding Dirichlet-to-Neumann operator as a first order classical pseudo-differential operator. Using the explicit representation of its symbol we prove an asymptotic expansion as the window length decreases.\"",
         "language" : "English",
         
         "bibtexKey": "hanel2017spectral"

      }
,
      {
         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2480eb8d27436d1813f64a75501305a78/elkepeter",         
         "tags" : [
            "Heisenberg","Kovarik","Laplacian","Ruszkowski","Spectral","estimates","iadm","weidl"
         ],
         
         "intraHash" : "480eb8d27436d1813f64a75501305a78",
         "interHash" : "a744d4ee0c0570857beee23ca1ced4b3",
         "label" : "Spectral estimates for the Heisenberg Laplacian on cylinders.",
         "user" : "elkepeter",
         "description" : "",
         "date" : "2021-10-08 20:07:59",
         "changeDate" : "2021-10-13 11:54:00",
         "count" : 2,
         "pub-type": "article",
         "journal": "Functional Analysis and Operator Theory for Quantum Physics, EMS Series of Congress Reports, J. Dittrich, et al. (eds.)",
         "year": "2017", 
         "url": "", 
         
         "author": [ 
            "Hynek Kovarik","Bartosch Ruszkowski","Timo Weidl"
         ],
         "authors": [
         	
            	{"first" : "Hynek",	"last" : "Kovarik"},
            	{"first" : "Bartosch",	"last" : "Ruszkowski"},
            	{"first" : "Timo",	"last" : "Weidl"}
         ],
         "pages": "433-446","abstract": "\"In this paper the authors consider the Heisenberg Laplacian in a domain Ω⊂ℝ3 with Dirichlet boundary conditions, formally given by\r\nA(Ω)=−X21−X22,\r\nwhere\r\nX1=∂x1+x22∂x3,X2=∂x2−x12∂x3.\r\n   The main result of the paper is a uniform upper bound with remainder of the quantity\r\nTr(A(Ω)−λ)−,\r\nthat is, the sum of all eigenvalues of A(Ω) smaller than λ, counted according to their multiplicities. \r\n   Previous and optimal results on the leading term were known from [A. M. Hansson and A. Laptev, in Groups and analysis, 100\u2013115, London Math. Soc. Lecture Note Ser., 354, Cambridge Univ. Press, Cambridge, 2008; MR2528463], and improved estimates were obtained in [H. Kovařík and T. Weidl, Proc. Roy. Soc. Edinburgh Sect. A 145 (2015), no. 1, 145\u2013160; MR3304579], where it was proved that for any bounded domain Ω⊂ℝ3 there exists a constant C(Ω)>0 such that\r\nTr(A(Ω)−λ)−≤max0,|Ω|96λ3−C(Ω)λ2.\r\n\r\n   In this paper, the authors improve the above estimate for cylindrical domains of the form Ω=ω×(a,b), where ω⊂ℝ2 is an open, simply connected, bounded set. Their main result (Theorem 2.3) is an estimate of the form\r\nTr(A(Ω)−λ)−≤max0,|Ω|96λ3−D(Ω)λ(2c+5)/(c+2),(1)\r\nwhere c is the best Hardy constant for ω, and the constant D(Ω) depends explicitly on the cylindrical domain Ω. Notice that the correction term in (1) is of order larger than λ2. \r\n   For cylinders Ω=ω×(a,b) with convex cross-section ω, the above estimate reads:\r\nTr(A(Ω)−λ)−≤max0,|Ω|96λ3−λ2+1/427⋅35/2|Ω|R(ω)3/2,\r\nwhere R(ω) is the Euclidean in-radius of ω. \r\n   The main techniques employed are the relation of A(Ω) with the magnetic Laplacian (with constant magnetic field) and Hardy inequalities.\"",
         "bibtexKey": "kovarik2017spectral"

      }
,
      {
         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/20e1f49c7962599f662210ebaff44b50b/elkepeter",         
         "tags" : [
            "Hänel","Spectral","Weidl","asymptotics","iadm"
         ],
         
         "intraHash" : "0e1f49c7962599f662210ebaff44b50b",
         "interHash" : "0e936fa8a9fa8b397cdce8f023e68e69",
         "label" : "Spectral asymptotics for the Dirichlet Laplacian with a Neumann window via a Birman-Schwinger analysis of the Dirichlet-to-Neumann operator.",
         "user" : "elkepeter",
         "description" : "",
         "date" : "2021-10-08 19:39:58",
         "changeDate" : "2021-10-13 11:54:00",
         "count" : 3,
         "pub-type": "article",
         "journal": "Functional Analysis and Operator Theory for Quantum Physics, EMS Series of Congress Reports, J. Dittrich, et al. (eds.)",
         "year": "2017", 
         "url": "", 
         
         "author": [ 
            "André Hänel","Timo Weidl"
         ],
         "authors": [
         	
            	{"first" : "André",	"last" : "Hänel"},
            	{"first" : "Timo",	"last" : "Weidl"}
         ],
         "pages": "315 - 352","abstract": "\"In the present article we will give a new proof of the ground state asymptotics of the Dirichlet Laplacian with a Neumann window acting on functions which are defined on a two-dimensional infinite strip or a three-dimensional infinite layer. The proof is based on the analysis of the corresponding Dirichlet-to-Neumann operator as a first order classical pseudo-differential operator. Using the explicit representation of its symbol we prove an asymptotic expansion as the window length decreases.\"",
         "language" : "English",
         
         "bibtexKey": "hanel2017spectral"

      }
,
      {
         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/25e886cb0a874a8dd5e3b896cf05536ee/b_schwederski",         
         "tags" : [
            "ESR","cation","cyclic","dialkylquinoxalinium","dialkylquinoxalinium;spectra","dialkylquinoxalinium;voltammetry","electrochem","property;redox","radical;quinoxalinium","spectral"
         ],
         
         "intraHash" : "5e886cb0a874a8dd5e3b896cf05536ee",
         "interHash" : "b93673563b609880f4569ba56a101a2d",
         "label" : "Electrochemical and spectroscopic characterization of N,N'-dialkylquinoxalinium redox systems",
         "user" : "b_schwederski",
         "description" : "",
         "date" : "2019-07-15 13:41:23",
         "changeDate" : "2019-07-15 11:42:10",
         "count" : 3,
         "pub-type": "article",
         "journal": "Chemische Berichte",
         "year": "1991", 
         "url": "", 
         
         "author": [ 
            "Andreas Schulz","Wolfgang. Kaim"
         ],
         "authors": [
         	
            	{"first" : "Andreas",	"last" : "Schulz"},
            	{"first" : "Wolfgang.",	"last" : "Kaim"}
         ],
         "volume": "124","number": "1","pages": "129--139","abstract": "The outstanding position of the 1,4-isomer, quinoxaline, among the diazanaphthalenes is confirmed by comparing LUMO energies from HMO perturbation calcns.  Diquaternary salts of quinoxaline, 2,3- and 6,7-dimethylquinoxaline and 2,3,6,7-tetramethylquinoxaline were isolated and characterized as compds. which are sensitive to redn. and hydrolysis.  Cyclic voltammetry of the two-step redox systems of the Weitz type showed two reversible one-electron redns. with an extraordinarily stable radical-cation intermediate (log Kc \\textgreater12).  The redox potentials are less neg. than those of the 4,4'-bipyridinium systems but also less pos. than those of N,N'-dialkylphenazinium compds.  The radical-cation intermediates, which include a TCNQ.bul.- salt, are characterized by ESR and by absorption spectroscopy in comparison to the resp. dications. [on SciFinder(R)]",
         "issn" : "0009-2940",
         
         "bibtexKey": "Schulz.1991"

      }
,
      {
         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/24b6636216b66dfdfd50ca53bb93685de/mathematik",         
         "tags" : [
            "(SUPG),","Galerkin,","Petrove-Galerkin","adaptive","conservation","continuous","discontinuous","from:mhartmann","hyperbolic","ians","laws,","method,","postprocessing","spectral","streamline","upwind","viscosity,","vorlaeufig","wavelet"
         ],
         
         "intraHash" : "4b6636216b66dfdfd50ca53bb93685de",
         "interHash" : "c8972e3ab25e760174ed7741330758be",
         "label" : "An adaptive wavelet space-time SUPG method for hyperbolic conservation\n\tlaws",
         "user" : "mathematik",
         "description" : "",
         "date" : "2018-07-20 10:54:20",
         "changeDate" : "2019-12-18 14:37:55",
         "count" : 2,
         "pub-type": "article",
         "journal": "Numerical Methods for Partial Differential Equations",
         "year": "2017", 
         "url": "https://onlinelibrary.wiley.com/doi/abs/10.1002/num.22180", 
         
         "author": [ 
            "Hadi Minbashian","Hojatolah Adibi","Mehdi Dehghan"
         ],
         "authors": [
         	
            	{"first" : "Hadi",	"last" : "Minbashian"},
            	{"first" : "Hojatolah",	"last" : "Adibi"},
            	{"first" : "Mehdi",	"last" : "Dehghan"}
         ],
         "volume": "33","number": "6","pages": "2062-2089","abstract": "This article concerns with incorporating wavelet bases into existing\n\tstreamline upwind Petrov-Galerkin (SUPG) methods for the numerical\n\tsolution of nonlinear hyperbolic conservation laws which are known\n\tto develop shock solutions. Here, we utilize an SUPG formulation\n\tusing continuous Galerkin in space and discontinuous Galerkin in\n\ttime. The main motivation for such a combination is that these methods\n\thave good stability properties thanks to adding diffusion in the\n\tdirection of streamlines. But they are more expensive than explicit\n\tsemidiscrete methods as they have to use space-time formulations.\n\tUsing wavelet bases we maintain the stability properties of SUPG\n\tmethods while we reduce the cost of these methods significantly through\n\tnatural adaptivity of wavelet expansions. In addition, wavelet bases\n\thave a hierarchical structure. We use this property to numerically\n\tinvestigate the hierarchical addition of an artificial diffusion\n\tfor further stabilization in spirit of spectral diffusion. Furthermore,\n\twe add the hierarchical diffusion only in the vicinity of discontinuities\n\tusing the feature of wavelet bases in detection of location of discontinuities.\n\tAlso, we again use the last feature of the wavelet bases to perform\n\ta postprocessing using a denosing technique based on a minimization\n\tformulation to reduce Gibbs oscillations near discontinuities while\n\tkeeping other regions intact. Finally, we show the performance of\n\tthe proposed combination through some numerical examples including\n\tBurgers�, transport, and wave equations as well as systems of shallow\n\twater equations.� 2017 Wiley Periodicals, Inc. Numer Methods Partial\n\tDifferential Eq 33: 2062�2089, 2017",
         "owner" : "seusdd",
         
         "doi" : "10.1002/num.22180",
         
         "eprint" : "https://onlinelibrary.wiley.com/doi/pdf/10.1002/num.22180",
         
         "bibtexKey": "minbashian2017adaptive"

      }
,
      {
         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/24b6636216b66dfdfd50ca53bb93685de/mhartmann",         
         "tags" : [
            "(SUPG),","Galerkin,","Petrove-Galerkin","adaptive","conservation","continuous","discontinuous","hyperbolic","laws,","method,","postprocessing","spectral","streamline","upwind","viscosity,","vorlaeufig","wavelet"
         ],
         
         "intraHash" : "4b6636216b66dfdfd50ca53bb93685de",
         "interHash" : "c8972e3ab25e760174ed7741330758be",
         "label" : "An adaptive wavelet space-time SUPG method for hyperbolic conservation\n\tlaws",
         "user" : "mhartmann",
         "description" : "",
         "date" : "2018-07-20 10:54:15",
         "changeDate" : "2018-07-20 08:54:15",
         "count" : 2,
         "pub-type": "article",
         "journal": "Numerical Methods for Partial Differential Equations",
         "year": "2017", 
         "url": "https://onlinelibrary.wiley.com/doi/abs/10.1002/num.22180", 
         
         "author": [ 
            "Hadi Minbashian","Hojatolah Adibi","Mehdi Dehghan"
         ],
         "authors": [
         	
            	{"first" : "Hadi",	"last" : "Minbashian"},
            	{"first" : "Hojatolah",	"last" : "Adibi"},
            	{"first" : "Mehdi",	"last" : "Dehghan"}
         ],
         "volume": "33","number": "6","pages": "2062-2089","abstract": "This article concerns with incorporating wavelet bases into existing\n\tstreamline upwind Petrov-Galerkin (SUPG) methods for the numerical\n\tsolution of nonlinear hyperbolic conservation laws which are known\n\tto develop shock solutions. Here, we utilize an SUPG formulation\n\tusing continuous Galerkin in space and discontinuous Galerkin in\n\ttime. The main motivation for such a combination is that these methods\n\thave good stability properties thanks to adding diffusion in the\n\tdirection of streamlines. But they are more expensive than explicit\n\tsemidiscrete methods as they have to use space-time formulations.\n\tUsing wavelet bases we maintain the stability properties of SUPG\n\tmethods while we reduce the cost of these methods significantly through\n\tnatural adaptivity of wavelet expansions. In addition, wavelet bases\n\thave a hierarchical structure. We use this property to numerically\n\tinvestigate the hierarchical addition of an artificial diffusion\n\tfor further stabilization in spirit of spectral diffusion. Furthermore,\n\twe add the hierarchical diffusion only in the vicinity of discontinuities\n\tusing the feature of wavelet bases in detection of location of discontinuities.\n\tAlso, we again use the last feature of the wavelet bases to perform\n\ta postprocessing using a denosing technique based on a minimization\n\tformulation to reduce Gibbs oscillations near discontinuities while\n\tkeeping other regions intact. Finally, we show the performance of\n\tthe proposed combination through some numerical examples including\n\tBurgers�, transport, and wave equations as well as systems of shallow\n\twater equations.� 2017 Wiley Periodicals, Inc. Numer Methods Partial\n\tDifferential Eq 33: 2062�2089, 2017",
         "owner" : "seusdd",
         
         "doi" : "10.1002/num.22180",
         
         "eprint" : "https://onlinelibrary.wiley.com/doi/pdf/10.1002/num.22180",
         
         "bibtexKey": "minbashian2017adaptive"

      }
	  
   ]
}