Pith. Sign in

RECORD

On the TVD property of second order methods for 2D scalar conservation laws

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Lilia Krivodonova, Alexey Smirnov

Numerical Analysis · Submitted 30 Sep 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We demonstrate numerically using the second order discontinuous Galerkin method that limited solutions of two-dimensional hyperbolic equations are TVD in means when total variation is computed using the new definition.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2110.00067 (version 3)
Pith ID5UBIOFEO, Pith's permanent record of this paper and its review
CitationAlexey Smirnov, Lilia Krivodonova. "On the TVD property of second order methods for 2D scalar conservation laws." arXiv:2110.00067 (2021). https://pith.science/paper/5UBIOFEO
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,285 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.24 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.52 · compares with prior results 0.88 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

The total variation diminishing (TVD) property is an important tool for ensuring nonlinear stability and convergence of numerical solutions of one-dimensional scalar conservation laws. However, it proved to be challenging to extend this approach to two-dimensional problems. Using the anisotropic definition for discrete total variation (TV), it was shown in \cite{Goodman} that TVD solutions of two-dimensional hyperbolic equations are at most first order accurate. We propose to use an alternative definition resulting from a full discretization of the semi-discrete Raviart-Thomas TV. We demonstrate numerically using the second order discontinuous Galerkin method that limited solutions of two-dimensional hyperbolic equations are TVD in means when total variation is computed using the new definition.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The total variation diminishing (TVD) property is an important tool for ensuring nonlinear stability and convergence of numerical solutions of one-dimensional scalar conservation laws. background 1.00 0.04 0.02 asserted 1.00
s1 However, it proved to be challenging to extend this approach to two-dimensional problems. gap 0.65 0.06 0.02 asserted 0.99
s2 Using the anisotropic definition for discrete total variation (TV), it was shown in \cite{Goodman} that TVD solutions of two-dimensional hyperbolic equations are at most first order accurate. background 0.92 0.03 0.06 asserted 1.00
s3 We propose to use an alternative definition resulting from a full discretization of the semi-discrete Raviart-Thomas TV. contribution 0.69 0.72 0.07 asserted 0.85
s4 We demonstrate numerically using the second order discontinuous Galerkin method that limited solutions of two-dimensional hyperbolic equations are TVD in means when total variation is computed using the new definition. result 0.97 0.96 0.83 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.75 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The total variation diminishing (TVD) property is an important tool for ensuring nonlinear stability and convergence of numerical solutions of one-dimensional scalar conservation laws. However, it proved to be challenging to extend this approach to two-dimensional problems. Using the anisotropic definition for discrete total variation (TV), it was shown in \cite{Goodman} that TVD solutions of two-dimensional hyperbolic equations are at most first order accurate. We propose to use an alternative definition resulting from a full discretization of the semi-discrete Raviart-Thomas TV. We demonstrate numerically using the second order discontinuous Galerkin method that limited solutions of two-dimensional hyperbolic equations are TVD in means when total variation is computed using the new definition.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.