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In this paper, we study the stabilizer-free weak Galerkin methods on polytopal meshes for a class of second order elliptic boundary value problems of divergence form and with gradient nonlinearity in the principal coefficient. With certain assumptions on the nonlinear coefficient, we show that the discrete problem has a unique solution. This is achieved by showing that the associated operator satisfies certain continuity and monotonicity properties. With the help of these properties, we derive optimal error estimates in the energy norm. We present several numerical examples to verify the error estimates.

A wide-band and high-resolution transmitter of optical isolation amplifier is proposed for switching power supply isolation and servo motor drive applications. The transmitter is based on the chopper-stabilized technique and sigma delta modulator. A built-in common-mode voltage circuit of switched capacitor is proposed to ensure the stability of input DC common mode. Meanwhile, the feedback capacitor is used to improve the driving ability, which helps to avoid a buffer with large input swing. The circuit is tapeout with GF CMOS 0.18 μm 1P6M process with 5 V power supply. The test results show that in 5 V supply voltage, the input swing of transmitter is 2 V and the effective signal bandwidth is 110 kHz. And the output resolution achieves 11 bit.