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• W2015311556 abstract "We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:mo>∇</mml:mo><mml:mi>u</mml:mi></mml:mrow></mml:math>belongs to the weaker<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mrow><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mi>Ω</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:mrow><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math>space taking the place of the classical<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mi mathvariant=bold-italic>H</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>div</mml:mi><mml:mo>;</mml:mo><mml:mi>Ω</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:mrow></mml:math>-norm for both the scalar unknown<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mrow><mml:mi>u</mml:mi></mml:mrow></mml:math>and the diffusion term<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mrow><mml:mi>w</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mi mathvariant=normal>Δ</mml:mi><mml:mi>u</mml:mi></mml:mrow></mml:math>and a priori error estimates in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mrow><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math>-norm for its gradient<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:mrow><mml:mi>χ</mml:mi><mml:mo>=</mml:mo><mml:mo>∇</mml:mo><mml:mi>u</mml:mi></mml:mrow></mml:math>for both semi-discrete and fully discrete schemes." @default.
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• W2015311556 date "2013-01-01" @default.
• W2015311556 modified "2023-10-15" @default.
• W2015311556 title "A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation" @default.
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• W2015311556 doi "https://doi.org/10.1155/2013/756281" @default.
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