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- W2084944524 abstract "In this paper a new approach is developed for analyzing the discontinuous Galerkin method for hyperbolic equations. For a model problem in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper R squared> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{R^2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the method is shown to converge at a rate <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper O left-parenthesis h Superscript n plus 1 Baseline right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>h</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>O({h^{n + 1}})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> when applied with <italic>n</italic>th degree polynomial approximations over a semiuniform triangulation, assuming sufficient regularity in the solution." @default.
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- W2084944524 date "1988-01-01" @default.
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- W2084944524 title "An optimal-order error estimate for the discontinuous Galerkin method" @default.
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- W2084944524 doi "https://doi.org/10.1090/s0025-5718-1988-0917819-3" @default.
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